Calculus of Variations and Geometric Measure Theory

E. Caputo - T. Rossi

First-order heat content asymptotics on ${\sf RCD}(K,N)$ spaces

created by rossi1 on 13 Dec 2022
modified on 18 Jan 2024

[BibTeX]

Published Paper

Inserted: 13 dec 2022
Last Updated: 18 jan 2024

Journal: Nonlinear Analysis
Year: 2023
Doi: https://doi.org/10.1016/j.na.2023.113385

ArXiv: 2212.06059 PDF

Abstract:

In this paper, we prove first-order asymptotics on a bounded open set of the heat content when the ambient space is an ${\sf RCD}(K,N)$ space, under a regularity condition for the boundary that we call measured interior geodesic condition of size $\epsilon$. We carefully study such a condition, relating it to the properties of the disintegration of the signed distance function from $\partial \Omega$ studied by Cavalletti and Mondino.