---
_id: '14934'
abstract:
- lang: eng
text: "We study random perturbations of a Riemannian manifold (M, g) by means of
so-called\r\nFractional Gaussian Fields, which are defined intrinsically by the
given manifold. The fields\r\nh• : ω \x02→ hω will act on the manifold via the
conformal transformation g \x02→ gω := e2hω g.\r\nOur focus will be on the regular
case with Hurst parameter H > 0, the critical case H = 0\r\nbeing the celebrated
Liouville geometry in two dimensions. We want to understand how basic\r\ngeometric
and functional-analytic quantities like diameter, volume, heat kernel, Brownian\r\nmotion,
spectral bound, or spectral gap change under the influence of the noise. And if
so, is\r\nit possible to quantify these dependencies in terms of key parameters
of the noise? Another\r\ngoal is to define and analyze in detail the Fractional
Gaussian Fields on a general Riemannian\r\nmanifold, a fascinating object of independent
interest."
acknowledgement: "The authors would like to thank Matthias Erbar and Ronan Herry for
valuable discussions on this project. They are also grateful to Nathanaël Berestycki,
and Fabrice Baudoin for respectively pointing out the references [7], and [6, 24],
and to Julien Fageot and Thomas Letendre for pointing out a mistake in a previous
version of the proof of Proposition 3.10. The authors feel very much indebted to
an anonymous reviewer for his/her careful reading and the many valuable suggestions
that have significantly contributed to the improvement of the paper. L.D.S. gratefully
acknowledges financial support by the Deutsche Forschungsgemeinschaft through CRC
1060 as well as through SPP 2265, and by the Austrian Science Fund (FWF) grant F65
at Institute of Science and Technology Austria. This research was funded in whole
or in part by the Austrian Science Fund (FWF) ESPRIT 208. For the purpose of open
access, the authors have applied a CC BY public copyright licence to any Author
Accepted Manuscript version arising from this submission. E.K. and K.-T.S. gratefully
acknowledge funding by the Deutsche Forschungsgemeinschaft through the Hausdorff
Center for Mathematics and through CRC 1060 as well as through SPP 2265.\r\nOpen
Access funding enabled and organized by Projekt DEAL."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Eva
full_name: Kopfer, Eva
last_name: Kopfer
- first_name: Karl Theodor
full_name: Sturm, Karl Theodor
last_name: Sturm
citation:
ama: Dello Schiavo L, Kopfer E, Sturm KT. A discovery tour in random Riemannian
geometry. Potential Analysis. 2024. doi:10.1007/s11118-023-10118-0
apa: Dello Schiavo, L., Kopfer, E., & Sturm, K. T. (2024). A discovery tour
in random Riemannian geometry. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-023-10118-0
chicago: Dello Schiavo, Lorenzo, Eva Kopfer, and Karl Theodor Sturm. “A Discovery
Tour in Random Riemannian Geometry.” Potential Analysis. Springer Nature,
2024. https://doi.org/10.1007/s11118-023-10118-0.
ieee: L. Dello Schiavo, E. Kopfer, and K. T. Sturm, “A discovery tour in random
Riemannian geometry,” Potential Analysis. Springer Nature, 2024.
ista: Dello Schiavo L, Kopfer E, Sturm KT. 2024. A discovery tour in random Riemannian
geometry. Potential Analysis.
mla: Dello Schiavo, Lorenzo, et al. “A Discovery Tour in Random Riemannian Geometry.”
Potential Analysis, Springer Nature, 2024, doi:10.1007/s11118-023-10118-0.
short: L. Dello Schiavo, E. Kopfer, K.T. Sturm, Potential Analysis (2024).
date_created: 2024-02-04T23:00:54Z
date_published: 2024-01-26T00:00:00Z
date_updated: 2024-02-05T13:04:23Z
day: '26'
department:
- _id: JaMa
doi: 10.1007/s11118-023-10118-0
language:
- iso: eng
main_file_link:
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url: https://doi.org/10.1007/s11118-023-10118-0
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Potential Analysis
publication_identifier:
eissn:
- 1572-929X
issn:
- 0926-2601
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A discovery tour in random Riemannian geometry
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '13145'
abstract:
- lang: eng
text: We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary
finite diffuse measure space. We provide an interpretation of this characterization
in analogy with the Mecke identity for Poisson point processes.
acknowledgement: Research supported by the Sfb 1060 The Mathematics of Emergent Effects
(University of Bonn). L.D.S. gratefully acknowledges funding of his current position
by the Austrian Science Fund (FWF) through project ESPRIT 208.
article_processing_charge: No
article_type: original
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Eugene
full_name: Lytvynov, Eugene
last_name: Lytvynov
citation:
ama: Dello Schiavo L, Lytvynov E. A Mecke-type characterization of the Dirichlet–Ferguson
measure. Electronic Communications in Probability. 2023;28:1-12. doi:10.1214/23-ECP528
apa: Dello Schiavo, L., & Lytvynov, E. (2023). A Mecke-type characterization
of the Dirichlet–Ferguson measure. Electronic Communications in Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/23-ECP528
chicago: Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization
of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability.
Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-ECP528.
ieee: L. Dello Schiavo and E. Lytvynov, “A Mecke-type characterization of the Dirichlet–Ferguson
measure,” Electronic Communications in Probability, vol. 28. Institute
of Mathematical Statistics, pp. 1–12, 2023.
ista: Dello Schiavo L, Lytvynov E. 2023. A Mecke-type characterization of the Dirichlet–Ferguson
measure. Electronic Communications in Probability. 28, 1–12.
mla: Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization
of the Dirichlet–Ferguson Measure.” Electronic Communications in Probability,
vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–12, doi:10.1214/23-ECP528.
short: L. Dello Schiavo, E. Lytvynov, Electronic Communications in Probability 28
(2023) 1–12.
date_created: 2023-06-18T22:00:48Z
date_published: 2023-05-05T00:00:00Z
date_updated: 2023-12-13T11:24:57Z
day: '05'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1214/23-ECP528
external_id:
isi:
- '001042025400001'
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- access_level: open_access
checksum: 4a543fe4b3f9e747cc52167c17bfb524
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creator: dernst
date_created: 2023-06-19T09:37:40Z
date_updated: 2023-06-19T09:37:40Z
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file_size: 271434
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intvolume: ' 28'
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month: '05'
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oa_version: Published Version
page: 1-12
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- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
publication: Electronic Communications in Probability
publication_identifier:
eissn:
- 1083-589X
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: A Mecke-type characterization of the Dirichlet–Ferguson measure
tmp:
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legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
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short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2023'
...
---
_id: '10145'
abstract:
- lang: eng
text: We study direct integrals of quadratic and Dirichlet forms. We show that each
quasi-regular Dirichlet space over a probability space admits a unique representation
as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same
underlying topology. The same holds for each quasi-regular strongly local Dirichlet
space over a metrizable Luzin σ-finite Radon measure space, and admitting carré
du champ operator. In this case, the representation is only projectively unique.
acknowledgement: The author is grateful to Professors Sergio Albeverio and Andreas
Eberle, and to Dr. Kohei Suzuki, for fruitful conversations on the subject of the
present work, and for respectively pointing out the references [1, 13], and [3,
20]. Finally, he is especially grateful to an anonymous Reviewer for their very
careful reading and their suggestions which improved the readability of the paper.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
citation:
ama: Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals
and applications. Potential Analysis. 2023;58:573-615. doi:10.1007/s11118-021-09951-y
apa: Dello Schiavo, L. (2023). Ergodic decomposition of Dirichlet forms via direct
integrals and applications. Potential Analysis. Springer Nature. https://doi.org/10.1007/s11118-021-09951-y
chicago: Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct
Integrals and Applications.” Potential Analysis. Springer Nature, 2023.
https://doi.org/10.1007/s11118-021-09951-y.
ieee: L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals
and applications,” Potential Analysis, vol. 58. Springer Nature, pp. 573–615,
2023.
ista: Dello Schiavo L. 2023. Ergodic decomposition of Dirichlet forms via direct
integrals and applications. Potential Analysis. 58, 573–615.
mla: Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct
Integrals and Applications.” Potential Analysis, vol. 58, Springer Nature,
2023, pp. 573–615, doi:10.1007/s11118-021-09951-y.
short: L. Dello Schiavo, Potential Analysis 58 (2023) 573–615.
date_created: 2021-10-17T22:01:17Z
date_published: 2023-03-01T00:00:00Z
date_updated: 2023-10-04T09:19:12Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s11118-021-09951-y
ec_funded: 1
external_id:
arxiv:
- '2003.01366'
isi:
- '000704213400001'
file:
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checksum: 625526482be300ca7281c91c30d41725
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creator: dernst
date_created: 2023-10-04T09:18:59Z
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file_size: 806391
relation: main_file
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has_accepted_license: '1'
intvolume: ' 58'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 573-615
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Potential Analysis
publication_identifier:
eissn:
- 1572-929X
issn:
- 0926-2601
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Ergodic decomposition of Dirichlet forms via direct integrals and applications
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 58
year: '2023'
...
---
_id: '12104'
abstract:
- lang: eng
text: We study ergodic decompositions of Dirichlet spaces under intertwining via
unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular
Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore,
every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces
is decomposable over their ergodic decompositions up to conjugation via an isomorphism
of the corresponding indexing spaces.
acknowledgement: Research supported by the Austrian Science Fund (FWF) grant F65 at
the Institute of Science and Technology Austria and by the European Research Council
(ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully
acknowledges funding of his current position by the Austrian Science Fund (FWF)
through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding
of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme
(Grant No. 156).
article_number: '9'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order
isomorphisms. Journal of Evolution Equations. 2023;23(1). doi:10.1007/s00028-022-00859-7
apa: Dello Schiavo, L., & Wirth, M. (2023). Ergodic decompositions of Dirichlet
forms under order isomorphisms. Journal of Evolution Equations. Springer
Nature. https://doi.org/10.1007/s00028-022-00859-7
chicago: Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of
Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations.
Springer Nature, 2023. https://doi.org/10.1007/s00028-022-00859-7.
ieee: L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms
under order isomorphisms,” Journal of Evolution Equations, vol. 23, no.
1. Springer Nature, 2023.
ista: Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms
under order isomorphisms. Journal of Evolution Equations. 23(1), 9.
mla: Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet
Forms under Order Isomorphisms.” Journal of Evolution Equations, vol. 23,
no. 1, 9, Springer Nature, 2023, doi:10.1007/s00028-022-00859-7.
short: L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).
date_created: 2023-01-08T23:00:53Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2023-06-28T11:54:35Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00028-022-00859-7
ec_funded: 1
external_id:
isi:
- '000906214600004'
file:
- access_level: open_access
checksum: 1f34f3e2cb521033de6154f274ea3a4e
content_type: application/pdf
creator: dernst
date_created: 2023-01-20T10:45:06Z
date_updated: 2023-01-20T10:45:06Z
file_id: '12325'
file_name: 2023_JourEvolutionEquations_DelloSchiavo.pdf
file_size: 422612
relation: main_file
success: 1
file_date_updated: 2023-01-20T10:45:06Z
has_accepted_license: '1'
intvolume: ' 23'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
- _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833
grant_number: ESP156_N
name: Gradient flow techniques for quantum Markov semigroups
publication: Journal of Evolution Equations
publication_identifier:
eissn:
- 1424-3202
issn:
- 1424-3199
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Ergodic decompositions of Dirichlet forms under order isomorphisms
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 23
year: '2023'
...
---
_id: '11354'
abstract:
- lang: eng
text: We construct a recurrent diffusion process with values in the space of probability
measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process
is associated with the Dirichlet form defined by integration of the Wasserstein
gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional
base spaces to the modified massive Arratia flow over the unit interval described
in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800).
Together with two different constructions of the process, we discuss its ergodicity,
invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics.
acknowledgement: Research supported by the Sonderforschungsbereich 1060 and the Hausdorff
Center for Mathematics. The author gratefully acknowledges funding of his current
position at IST Austria by the Austrian Science Fund (FWF) grant F65 and by the
European Research Council (ERC, Grant agreement No. 716117, awarded to Prof. Dr.
Jan Maas).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
citation:
ama: Dello Schiavo L. The Dirichlet–Ferguson diffusion on the space of probability
measures over a closed Riemannian manifold. Annals of Probability. 2022;50(2):591-648.
doi:10.1214/21-AOP1541
apa: Dello Schiavo, L. (2022). The Dirichlet–Ferguson diffusion on the space of
probability measures over a closed Riemannian manifold. Annals of Probability.
Institute of Mathematical Statistics. https://doi.org/10.1214/21-AOP1541
chicago: Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space
of Probability Measures over a Closed Riemannian Manifold.” Annals of Probability.
Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1541.
ieee: L. Dello Schiavo, “The Dirichlet–Ferguson diffusion on the space of probability
measures over a closed Riemannian manifold,” Annals of Probability, vol.
50, no. 2. Institute of Mathematical Statistics, pp. 591–648, 2022.
ista: Dello Schiavo L. 2022. The Dirichlet–Ferguson diffusion on the space of probability
measures over a closed Riemannian manifold. Annals of Probability. 50(2), 591–648.
mla: Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability
Measures over a Closed Riemannian Manifold.” Annals of Probability, vol.
50, no. 2, Institute of Mathematical Statistics, 2022, pp. 591–648, doi:10.1214/21-AOP1541.
short: L. Dello Schiavo, Annals of Probability 50 (2022) 591–648.
date_created: 2022-05-08T22:01:44Z
date_published: 2022-03-01T00:00:00Z
date_updated: 2023-10-17T12:50:24Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/21-AOP1541
ec_funded: 1
external_id:
arxiv:
- '1811.11598'
isi:
- '000773518500005'
intvolume: ' 50'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.1811.11598'
month: '03'
oa: 1
oa_version: Preprint
page: 591-648
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Annals of Probability
publication_identifier:
eissn:
- 2168-894X
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Dirichlet–Ferguson diffusion on the space of probability measures over
a closed Riemannian manifold
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 50
year: '2022'
...
---
_id: '10588'
abstract:
- lang: eng
text: We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying
the quasi curvature-dimension condition recently introduced in Milman (Commun
Pure Appl Math, to appear). We provide several applications to properties of the
corresponding heat semigroup. In particular, under the additional assumption of
infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the
heat semigroup with respect to the distance, and prove the irreducibility of the
heat semigroup. These results apply in particular to large classes of (ideal)
sub-Riemannian manifolds.
acknowledgement: "The authors are grateful to Dr. Bang-Xian Han for helpful discussions
on the Sobolev-to-Lipschitz property on metric measure spaces, and to Professor
Kazuhiro Kuwae, Professor Emanuel Milman, Dr. Giorgio Stefani, and Dr. Gioacchino
Antonelli for reading a preliminary version of this work and for their valuable
comments and suggestions. Finally, they wish to express their gratitude to two anonymous
Reviewers whose suggestions improved the presentation of this work.\r\n\r\nL.D.S.
gratefully acknowledges funding of his position by the Austrian Science Fund (FWF)
grant F65, and by the European Research Council (ERC, grant No. 716117, awarded
to Prof. Dr. Jan Maas).\r\n\r\nK.S. gratefully acknowledges funding by: the JSPS
Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research
Center Initiative (WPI), MEXT, Japan; JSPS Grant-in-Aid for Scientific Research
on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number
17H06465; and the Alexander von Humboldt Stiftung, Humboldt-Forschungsstipendium."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Kohei
full_name: Suzuki, Kohei
last_name: Suzuki
citation:
ama: Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and
applications. Mathematische Annalen. 2022;384:1815-1832. doi:10.1007/s00208-021-02331-2
apa: Dello Schiavo, L., & Suzuki, K. (2022). Sobolev-to-Lipschitz property on
QCD- spaces and applications. Mathematische Annalen. Springer Nature. https://doi.org/10.1007/s00208-021-02331-2
chicago: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property
on QCD- Spaces and Applications.” Mathematische Annalen. Springer Nature,
2022. https://doi.org/10.1007/s00208-021-02331-2.
ieee: L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces
and applications,” Mathematische Annalen, vol. 384. Springer Nature, pp.
1815–1832, 2022.
ista: Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces
and applications. Mathematische Annalen. 384, 1815–1832.
mla: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on
QCD- Spaces and Applications.” Mathematische Annalen, vol. 384, Springer
Nature, 2022, pp. 1815–32, doi:10.1007/s00208-021-02331-2.
short: L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832.
date_created: 2022-01-02T23:01:35Z
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keyword:
- quasi curvature-dimension condition
- sub-riemannian geometry
- Sobolev-to-Lipschitz property
- Varadhan short-time asymptotics
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title: Sobolev-to-Lipschitz property on QCD- spaces and applications
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---
_id: '12177'
abstract:
- lang: eng
text: Using elementary hyperbolic geometry, we give an explicit formula for the
contraction constant of the skinning map over moduli spaces of relatively acylindrical
hyperbolic manifolds.
acknowledgement: "The first author was partially supported by the National Science
Foundation under Grant\r\nNo. DMS-1928930 while participating in a program hosted
by the Mathematical Sciences Research Institute in Berkeley, California, during
the Fall 2020 semester. The second author gratefully acknowledges funding by the
Austrian Science Fund (FWF) through grants F65 and ESPRIT 208, by the European Research
Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas), and by the Deutsche
Forschungsgemeinschaft through the SPP 2265."
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author:
- first_name: Tommaso
full_name: Cremaschi, Tommaso
last_name: Cremaschi
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
citation:
ama: Cremaschi T, Dello Schiavo L. Effective contraction of Skinning maps. Proceedings
of the American Mathematical Society, Series B. 2022;9(43):445-459. doi:10.1090/bproc/134
apa: Cremaschi, T., & Dello Schiavo, L. (2022). Effective contraction of Skinning
maps. Proceedings of the American Mathematical Society, Series B. American
Mathematical Society. https://doi.org/10.1090/bproc/134
chicago: Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of
Skinning Maps.” Proceedings of the American Mathematical Society, Series B.
American Mathematical Society, 2022. https://doi.org/10.1090/bproc/134.
ieee: T. Cremaschi and L. Dello Schiavo, “Effective contraction of Skinning maps,”
Proceedings of the American Mathematical Society, Series B, vol. 9, no.
43. American Mathematical Society, pp. 445–459, 2022.
ista: Cremaschi T, Dello Schiavo L. 2022. Effective contraction of Skinning maps.
Proceedings of the American Mathematical Society, Series B. 9(43), 445–459.
mla: Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning
Maps.” Proceedings of the American Mathematical Society, Series B, vol.
9, no. 43, American Mathematical Society, 2022, pp. 445–59, doi:10.1090/bproc/134.
short: T. Cremaschi, L. Dello Schiavo, Proceedings of the American Mathematical
Society, Series B 9 (2022) 445–459.
date_created: 2023-01-12T12:12:17Z
date_published: 2022-11-02T00:00:00Z
date_updated: 2023-01-26T13:04:13Z
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doi: 10.1090/bproc/134
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intvolume: ' 9'
issue: '43'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '11'
oa: 1
oa_version: Published Version
page: 445-459
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
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call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Proceedings of the American Mathematical Society, Series B
publication_identifier:
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publisher: American Mathematical Society
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title: Effective contraction of Skinning maps
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...
---
_id: '10070'
abstract:
- lang: eng
text: We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties
for generalized intrinsic distances on strongly local Dirichlet spaces possibly
without square field operator. We present many non-smooth and infinite-dimensional
examples. As an application, we prove the integral Varadhan short-time asymptotic
with respect to a given distance function for a large class of strongly local
Dirichlet forms.
acknowledgement: 'The authors are grateful to Professor Kazuhiro Kuwae for kindly
providing a copy of [49]. They are also grateful to Dr. Bang-Xian Han for helpful
discussions on the Sobolev-to-Lipschitz property on metric measure spaces. They
wish to express their deepest gratitude to an anonymous Reviewer, whose punctual
remarks and comments greatly improved the accessibility and overall quality of the
initial submission. This work was completed while L.D.S. was a member of the Institut
für Angewandte Mathematik of the University of Bonn. He acknowledges funding of
his position at that time by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) through the Sonderforschungsbereich (Sfb, Collaborative Research Center)
1060 - project number 211504053. He also acknowledges funding of his current position
by the Austrian Science Fund (FWF) grant F65, and by the European Research Council
(ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas). K.S. gratefully acknowledges
funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier
International Research Center Initiative (WPI), MEXT, Japan; and JSPS Grant-in-Aid
for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials
Design”, Grant Number 17H06465.'
article_number: '109234'
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article_type: original
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Kohei
full_name: Suzuki, Kohei
last_name: Suzuki
citation:
ama: Dello Schiavo L, Suzuki K. Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces. Journal of Functional Analysis.
2021;281(11). doi:10.1016/j.jfa.2021.109234
apa: Dello Schiavo, L., & Suzuki, K. (2021). Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces. Journal of Functional Analysis.
Elsevier. https://doi.org/10.1016/j.jfa.2021.109234
chicago: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and
Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” Journal
of Functional Analysis. Elsevier, 2021. https://doi.org/10.1016/j.jfa.2021.109234.
ieee: L. Dello Schiavo and K. Suzuki, “Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces,” Journal of Functional Analysis,
vol. 281, no. 11. Elsevier, 2021.
ista: Dello Schiavo L, Suzuki K. 2021. Rademacher-type theorems and Sobolev-to-Lipschitz
properties for strongly local Dirichlet spaces. Journal of Functional Analysis.
281(11), 109234.
mla: Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz
Properties for Strongly Local Dirichlet Spaces.” Journal of Functional Analysis,
vol. 281, no. 11, 109234, Elsevier, 2021, doi:10.1016/j.jfa.2021.109234.
short: L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021).
date_created: 2021-10-03T22:01:21Z
date_published: 2021-09-15T00:00:00Z
date_updated: 2023-08-14T07:05:44Z
day: '15'
department:
- _id: JaMa
doi: 10.1016/j.jfa.2021.109234
ec_funded: 1
external_id:
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- '2008.01492'
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- '000703896600005'
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issue: '11'
language:
- iso: eng
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url: https://doi.org/10.48550/arXiv.2008.01492
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Journal of Functional Analysis
publication_identifier:
eissn:
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issn:
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publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
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title: Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local
Dirichlet spaces
type: journal_article
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...