The Anisotropic Gaussian Isoperimetric Inequality and Ehrhard Symmetrization

Speaker:Dr.  Kuan-Ting Yeh, University of Washingtom

Title: The Anisotropic Gaussian Isoperimetric Inequality and Ehrhard Symmetrization

Abstract:

The Gaussian isoperimetric problem holds significant relevance across various fields, with Ehrhard symmetrization serving as a crucial tool in its examination. One natural question to ask is if we can extend those concepts to anisotropic Gaussian measures. In this talk, we show analogous results about the anisotropic Gaussian isoperimetric problem. In addition, we uncover an example highlighting a scenario where Ehrhard symmetrization fails to decrease the anisotropic Gaussian perimeter, thereby introducing a novel inequality that incorporates an error term. Finally, we present that within specific classes, only the isotropic Gaussian measure satisfies the perimeter-decreasing property under symmetrization.

Zoom Link:

https://oist.zoom.us/j/95466328785?pwd=MW9kbjZ1THlESDhzd2p0anNPazF2dz09