Work

Power concavity and Dirichlet heat flow

Year: 2021

Type: preprint

Abstract: We show that log-concavity is the weakest power concavity preserved by the Dirichlet heat flow in $N$-dimensional convex domains, where $N\ge 2$ (indeed, we prove that starting with a negative power concave initial datum may result in losing immediately any reminiscence of concavity). Jointly with what we already know, i.e. that log-concavity is the strongest power concavity preserved by the Dirichlet heat flow, we see that log-concavity is indeed the only power concavity preserved by the Dirichlet heat flow.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2105.02574

Authors: Ishige, Kazuhiro, Salani, Paolo, Takatsu, Asuka

Institutions: The University of Tokyo, University of Florence, Tokyo Metropolitan University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W3157787783

Cites: 8

Cited by:

Related to: 10