Applied Math Seminar- Structure of Measures for which Ehrhard Symmetrization is Perimeter-Decreasing

Title: Structure of Measures for which Ehrhard Symmetrization is Perimeter-Decreasing

 

Abstract: In Euclidean space, Steiner transformed a region in a way that reduced its perimeter while preserving its area. An analogous symmetrization technique for the Gaussian measure was later developed by Ehrhard and plays a crucial role in analysis. A natural question arises: Are there other finite measures that share this property? We present an example where this property fails. Furthermore, we show that within a broad class of finite measures, the isotropic Gaussian measure is the only one that satisfies this property. This talk is partially based on a joint work with Sean McCurdy.