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arXiv · 2306.04522

A remark on a conjecture on the symmetric Gaussian Problem

Nicola Fusco·Domenico Angelo La Manna
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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.

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Nicola Fusco, Domenico Angelo La Manna. 2023-06-07. A remark on a conjecture on the symmetric Gaussian Problem. https://doi.org/10.1017/s0013091524000221

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