Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591384 | Journal of Functional Analysis | 2010 | 26 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory