A remark on a conjecture on the symmetric Gaussian Problem

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.

References in corpus (1)

• Convex Cylinders and the Symmetric Gaussian Isoperimetric Problem

Cited by in corpus (1)

• Liquid drop with capillarity and rotating traveling waves