A remark on a conjecture on the symmetric Gaussian Problem
Analysis of PDEs
2024-05-22 v2
Abstract
In this paper we study the functional given by the integral of the mean curvature of a convex set with Gaussian weight with Gaussian volume constraint. It was conjectured that the ball centered at the origin is the only minimizer of such a functional for certain value of the mass. We give a positive answer in dimension two while in higher dimension the situation is different. In fact, for small value of mass the ball centered at the origin is a local minimizer while for large values the ball is a maximizer among convex sets with uniform bound on the curvature.
Keywords
Cite
@article{arxiv.2306.04522,
title = {A remark on a conjecture on the symmetric Gaussian Problem},
author = {Nicola Fusco and Domenico Angelo La Manna},
journal= {arXiv preprint arXiv:2306.04522},
year = {2024}
}