English

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}
}

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58 pages