Gradient estimates for the heat equation under the Ricci flow

Details Gradient estimates for the heat equation under the Ricci flow Gradient estimates for the heat equation under the Ricci flow

2009-10-06

arxiv.org/abs/0910.1053v2

Journal of Functional Analysis 258 (2010), pages 3517-3542

Mathematics

Differential Geometry

21 pages, 2 figures

Scientific paper

10.1016/j.jfa.2009.12.003

The paper considers a manifold $M$ evolving under the Ricci flow and establishes a series of gradient estimates for positive solutions of the heat equation on $M$. Among other results, we prove Li-Yau-type inequalities in this context. We consider both the case where $M$ is a complete manifold without boundary and the case where $M$ is a compact manifold with boundary. Applications of our results include Harnack inequalities for the heat equation on $M$.

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