preprint

Inserted: 11 jul 2023
Last Updated: 12 sep 2024

Journal: Proceedings of the Edinburgh Mathematical Society
Volume: 67
Number: 2
Pages: 643-661.
Year: 2023
Doi: doi:10.1017/S0013091524000221

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.