Fractal curvatures and short-time asymptotics of heat content
Analysis of PDEs
2025-08-19 v2 Mathematical Physics
Differential Geometry
Functional Analysis
math.MP
Abstract
The aim of our paper is twofold. First, we present new mathematical developments on the analysis of de Gennes' hypothesis on the short-time asymptotics of the heat content for bounded domains with smooth boundary and with fractal boundary. Second, we discuss new findings and concepts related to fractal curvatures for domains with fractal boundary. We conjecture that fractal curvatures and their scaling exponents will emerge in the short-time heat content asymptotics of domains with fractal boundary and the results discussed here are small initial contributions towards a resolution.
Keywords
Cite
@article{arxiv.2502.02989,
title = {Fractal curvatures and short-time asymptotics of heat content},
author = {Anna Rozanova-Pierrat and Alexander Teplyaev and Steffen Winter and Martina Zähle},
journal= {arXiv preprint arXiv:2502.02989},
year = {2025}
}