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Anisotropic Gaussian Measures and Ehrhard Symmetrization

Kuan-Ting Yeh, University of Washington
Thursday, February 1, 2024 - 12:30pm to 1:20pm
PDL C-401

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 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.