Heat flow within convex sets
Differential Geometry
2025-04-04 v2 Analysis of PDEs
Abstract
A solution to the heat equation between Riemannian manifolds, where the domain is compact and possibly has boundary, will not leave a compact and locally convex set before the image of the boundary does.
Keywords
Cite
@article{arxiv.1412.0347,
title = {Heat flow within convex sets},
author = {James Dibble},
journal= {arXiv preprint arXiv:1412.0347},
year = {2025}
}
Comments
8 pages; added discussion of the strong maximum principle, background information on viscosity solutions, and some references; other minor edits throughout