---
_id: '12764'
abstract:
- lang: eng
  text: We study a new discretization of the Gaussian curvature for polyhedral surfaces.
    This discrete Gaussian curvature is defined on each conical singularity of a polyhedral
    surface as the quotient of the angle defect and the area of the Voronoi cell corresponding
    to the singularity. We divide polyhedral surfaces into discrete conformal classes
    using a generalization of discrete conformal equivalence pioneered by Feng Luo.
    We subsequently show that, in every discrete conformal class, there exists a polyhedral
    surface with constant discrete Gaussian curvature. We also provide explicit examples
    to demonstrate that this surface is in general not unique.
acknowledgement: Open access funding provided by the Austrian Science Fund (FWF).
  This research was supported by the FWF grant, Project number I4245-N35, and by the
  Deutsche Forschungsgemeinschaft (DFG - German Research Foundation) - Project-ID
  195170736 - TRR109.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Hana
  full_name: Kourimska, Hana
  id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
  last_name: Kourimska
  orcid: 0000-0001-7841-0091
citation:
  ama: Kourimska H. Discrete yamabe problem for polyhedral surfaces. <i>Discrete and
    Computational Geometry</i>. 2023;70:123-153. doi:<a href="https://doi.org/10.1007/s00454-023-00484-2">10.1007/s00454-023-00484-2</a>
  apa: Kourimska, H. (2023). Discrete yamabe problem for polyhedral surfaces. <i>Discrete
    and Computational Geometry</i>. Springer Nature. <a href="https://doi.org/10.1007/s00454-023-00484-2">https://doi.org/10.1007/s00454-023-00484-2</a>
  chicago: Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” <i>Discrete
    and Computational Geometry</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s00454-023-00484-2">https://doi.org/10.1007/s00454-023-00484-2</a>.
  ieee: H. Kourimska, “Discrete yamabe problem for polyhedral surfaces,” <i>Discrete
    and Computational Geometry</i>, vol. 70. Springer Nature, pp. 123–153, 2023.
  ista: Kourimska H. 2023. Discrete yamabe problem for polyhedral surfaces. Discrete
    and Computational Geometry. 70, 123–153.
  mla: Kourimska, Hana. “Discrete Yamabe Problem for Polyhedral Surfaces.” <i>Discrete
    and Computational Geometry</i>, vol. 70, Springer Nature, 2023, pp. 123–53, doi:<a
    href="https://doi.org/10.1007/s00454-023-00484-2">10.1007/s00454-023-00484-2</a>.
  short: H. Kourimska, Discrete and Computational Geometry 70 (2023) 123–153.
date_created: 2023-03-26T22:01:09Z
date_published: 2023-07-01T00:00:00Z
date_updated: 2023-10-04T11:46:48Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.1007/s00454-023-00484-2
external_id:
  isi:
  - '000948148000001'
file:
- access_level: open_access
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  creator: dernst
  date_created: 2023-10-04T11:46:24Z
  date_updated: 2023-10-04T11:46:24Z
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  file_size: 1026683
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has_accepted_license: '1'
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language:
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month: '07'
oa: 1
oa_version: Published Version
page: 123-153
project:
- _id: 26AD5D90-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I04245
  name: Algebraic Footprints of Geometric Features in Homology
publication: Discrete and Computational Geometry
publication_identifier:
  eissn:
  - 1432-0444
  issn:
  - 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Discrete yamabe problem for polyhedral surfaces
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: 70
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...
---
_id: '10071'
alternative_title:
- Early Career
article_processing_charge: No
article_type: letter_note
author:
- first_name: Henry
  full_name: Adams, Henry
  last_name: Adams
- first_name: Hana
  full_name: Kourimska, Hana
  id: D9B8E14C-3C26-11EA-98F5-1F833DDC885E
  last_name: Kourimska
- first_name: Teresa
  full_name: Heiss, Teresa
  id: 4879BB4E-F248-11E8-B48F-1D18A9856A87
  last_name: Heiss
  orcid: 0000-0002-1780-2689
- first_name: Sarah
  full_name: Percival, Sarah
  last_name: Percival
- first_name: Lori
  full_name: Ziegelmeier, Lori
  last_name: Ziegelmeier
citation:
  ama: Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. How to tutorial-a-thon.
    <i>Notices of the American Mathematical Society</i>. 2021;68(9):1511-1514. doi:<a
    href="https://doi.org/10.1090/noti2349">10.1090/noti2349</a>
  apa: Adams, H., Kourimska, H., Heiss, T., Percival, S., &#38; Ziegelmeier, L. (2021).
    How to tutorial-a-thon. <i>Notices of the American Mathematical Society</i>. American
    Mathematical Society. <a href="https://doi.org/10.1090/noti2349">https://doi.org/10.1090/noti2349</a>
  chicago: Adams, Henry, Hana Kourimska, Teresa Heiss, Sarah Percival, and Lori Ziegelmeier.
    “How to Tutorial-a-Thon.” <i>Notices of the American Mathematical Society</i>.
    American Mathematical Society, 2021. <a href="https://doi.org/10.1090/noti2349">https://doi.org/10.1090/noti2349</a>.
  ieee: H. Adams, H. Kourimska, T. Heiss, S. Percival, and L. Ziegelmeier, “How to
    tutorial-a-thon,” <i>Notices of the American Mathematical Society</i>, vol. 68,
    no. 9. American Mathematical Society, pp. 1511–1514, 2021.
  ista: Adams H, Kourimska H, Heiss T, Percival S, Ziegelmeier L. 2021. How to tutorial-a-thon.
    Notices of the American Mathematical Society. 68(9), 1511–1514.
  mla: Adams, Henry, et al. “How to Tutorial-a-Thon.” <i>Notices of the American Mathematical
    Society</i>, vol. 68, no. 9, American Mathematical Society, 2021, pp. 1511–14,
    doi:<a href="https://doi.org/10.1090/noti2349">10.1090/noti2349</a>.
  short: H. Adams, H. Kourimska, T. Heiss, S. Percival, L. Ziegelmeier, Notices of
    the American Mathematical Society 68 (2021) 1511–1514.
date_created: 2021-10-03T22:01:22Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2021-12-03T07:31:26Z
day: '01'
department:
- _id: HeEd
doi: 10.1090/noti2349
intvolume: '        68'
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://www.ams.org/notices/
month: '10'
oa: 1
oa_version: Published Version
page: 1511-1514
publication: Notices of the American Mathematical Society
publication_identifier:
  eissn:
  - 1088-9477
  issn:
  - 0002-9920
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: How to tutorial-a-thon
type: journal_article
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 68
year: '2021'
...