A geometric approach for convexity in some variational problem in the Gauss space

TL;DR

This paper proves the convexity of minimizers for certain variational problems in Gauss space using a geometric adaptation of Korevaar's classical argument.

Contribution

It introduces a geometric approach to establish convexity of solutions in Gauss space, extending previous methods to this setting.

Findings

Minimizers in Gauss space are convex under certain variational conditions.

The proof adapts Korevaar's argument geometrically for the Gauss space context.

The approach provides a new perspective on convexity in variational problems.

Abstract

In this short note we prove the convexity of minimizers of some variational problem in the Gauss space. This proof is based on a geometric version of an older argument due to Korevaar.