Calculus of Variations and Geometric Measure Theory

N. Fusco - D. A. La Manna

A remark on a conjecture on the symmetric Gaussian Problem

created by lamanna on 11 Jul 2023



Inserted: 11 jul 2023

Year: 2023

ArXiv: 2306.04522 PDF


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.