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

Emanuele Caputo; Tommaso Rossi

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

Metric Geometry 2022-12-13 v1 Analysis of PDEs Differential Geometry

Authors: Emanuele Caputo , Tommaso Rossi

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.

Keywords

heat content asymptotics rcd spaces measured interior geodesic condition signed distance function disintegration

Cite

@article{arxiv.2212.06059,
  title  = {First-order heat content asymptotics on ${\sf RCD}(K,N)$ spaces},
  author = {Emanuele Caputo and Tommaso Rossi},
  journal= {arXiv preprint arXiv:2212.06059},
  year   = {2022}
}

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46 pages, 2 figures

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

Abstract

Keywords

Cite

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