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Preservation of F-convexity under the heat flow

Kazuhiro Ishige, Troy Petitt, Paolo Salani

Abstract

We introduce the notion of F-convexity as a general extension of power convexity. We characterize the F-convexities preserved under the heat flow in the n-dimensional Euclidean space, and identify the strongest and the weakest ones among them. We also characterize the F-convexities preserved under the Dirichlet heat flow in convex domains.

Preservation of F-convexity under the heat flow

Abstract

We introduce the notion of F-convexity as a general extension of power convexity. We characterize the F-convexities preserved under the heat flow in the n-dimensional Euclidean space, and identify the strongest and the weakest ones among them. We also characterize the F-convexities preserved under the Dirichlet heat flow in convex domains.
Paper Structure (5 sections, 114 equations)

This paper contains 5 sections, 114 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proof of Theorems \ref{['Theorem:1.1']} and \ref{['Theorem:1.2']}
  4. Preservation of $F$-convexity without any sign restriction
  5. Preservation of $F$-convexity under the Dirichlet heat flow