Differential Harnack Estimates for Backward Heat Equations with Potentials under the Ricci Flow
Differential Geometry
2008-05-23 v1
Abstract
In this paper, we derive a general evolution formula for possible Harnack quantities. As a consequence, we prove several differential Harnack inequalities for positive solutions of backward heat-type equations with potentials (including the conjugate heat equation) under the Ricci flow. We shall also derive Perelman's Harnack inequality for the fundamental solution of the conjugate heat equation under the Ricci flow.
Keywords
Cite
@article{arxiv.0805.3381,
title = {Differential Harnack Estimates for Backward Heat Equations with Potentials under the Ricci Flow},
author = {Xiaodong Cao},
journal= {arXiv preprint arXiv:0805.3381},
year = {2008}
}
Comments
13 pages