Isoperimetry and Stability of Hyperplanes for Product Probability Measures

TL;DR

This paper studies the stability of half-spaces as isoperimetric sets in product probability measures, focusing on coordinate and non-coordinate cases, with applications to the logistic measure.

Contribution

It provides new insights into the stability of half-spaces for product measures, including specific results for the logistic measure, expanding understanding of isoperimetric problems.

Findings

Characterization of stable half-spaces for product measures

Application of results to logistic measure examples

Analysis of coordinate and non-coordinate half-spaces

Abstract

We investigate stationarity and stability of half-spaces as isoperimetric sets for product probability measures, considering the cases of coordinate and non-coordinate half-spaces. Moreover, we present several examples to which our results can be applied, with a particular emphasis on the logistic measure.