Optimal Hamilton-type gradient estimates for the heat equation on noncompact manifolds
Analysis of PDEs
2025-07-17 v1 Differential Geometry
Abstract
We derive localized and global noncompact versions of Hamilton's gradient estimate for positive solutions to the heat equation on Riemannian manifolds with Ricci curvature bounded below. Our estimates are essentially optimal and significantly improve on all previous estimates of this type. As applications, we derive a new and sharp, space only, local pseudo-Harnack inequality, as well as estimates of the spatial modulus of continuity of solutions.
Keywords
Cite
@article{arxiv.2507.12190,
title = {Optimal Hamilton-type gradient estimates for the heat equation on noncompact manifolds},
author = {Loth Damagui Chabi and Philippe Souplet},
journal= {arXiv preprint arXiv:2507.12190},
year = {2025}
}