@inbook{74,
  abstract     = {We study the Gromov waist in the sense of t-neighborhoods for measures in the Euclidean  space,  motivated  by  the  famous  theorem  of  Gromov  about  the  waist  of  radially symmetric Gaussian measures.  In particular, it turns our possible to extend Gromov’s original result  to  the  case  of  not  necessarily  radially  symmetric  Gaussian  measure.   We  also  provide examples of measures having no t-neighborhood waist property, including a rather wide class
of compactly supported radially symmetric measures and their maps into the Euclidean space of dimension at least 2.
We  use  a  simpler  form  of  Gromov’s  pancake  argument  to  produce  some  estimates  of t-neighborhoods of (weighted) volume-critical submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic manifolds in the complex projective space. In the appendix of this paper we provide for reader’s convenience a more detailed explanation of the Caffarelli theorem that we use to handle not necessarily radially symmetric Gaussian
measures.},
  author       = {Akopyan, Arseniy and Karasev, Roman},
  booktitle    = {Geometric Aspects of Functional Analysis},
  editor       = {Klartag, Bo'az and Milman, Emanuel},
  isbn         = {9783030360191},
  issn         = {16179692},
  pages        = {1--27},
  publisher    = {Springer Nature},
  title        = {{Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures}},
  doi          = {10.1007/978-3-030-36020-7_1},
  volume       = {2256},
  year         = {2020},
}