Hamilton's Gradient Estimates and A Monotonicity Formula for Heat Flows on Metric Measure Spaces
Metric Geometry
2015-12-29 v1 Differential Geometry
Abstract
In this paper, we extend the Hamilton's gradient estimates \cite{har93} and a monotonicity formula of entropy \cite{ni04} for heat flows from smooth Riemannian manifolds to (non-smooth) metric measure spaces with appropriate Riemannian curvature-dimension condition.
Keywords
Cite
@article{arxiv.1512.08306,
title = {Hamilton's Gradient Estimates and A Monotonicity Formula for Heat Flows on Metric Measure Spaces},
author = {Renjin Jiang and Huichun Zhang},
journal= {arXiv preprint arXiv:1512.08306},
year = {2015}
}
Comments
19 pages, In a special issue of Nonlinear Analysis (vol 131,2016,32-47): Qualitative and Quantitative Properties of Solutions to Parabolic Equations,in Honor of Victor A. Galaktionov for his 60th Birthday, Edited By Thierry Coulhon, Neil Trudinger and Vincenzo Vespri