The Anisotropic Gaussian Isoperimetric Inequality and Ehrhard Symmetrization
Probability
2023-09-26 v2 Analysis of PDEs
Abstract
In this paper, we prove the isoperimetric inequality for the anisotropic Gaussian measure and characterize the cases of equality. We also find an example that shows Ehrhard symmetrization fails to decrease for the anisotropic Gaussian perimeter and gives a new inequality that includes an error term. This new inequality, in particular, gives us a hint to prove a uniqueness result for the anisotropic Ehrhard symmetrization.
Keywords
Cite
@article{arxiv.2309.03853,
title = {The Anisotropic Gaussian Isoperimetric Inequality and Ehrhard Symmetrization},
author = {Kuan-Ting Yeh},
journal= {arXiv preprint arXiv:2309.03853},
year = {2023}
}
Comments
58 pages