Gradient estimates for the heat equation under the Ricci flow |
| |
Authors: | Mihai Bailesteanu |
| |
Affiliation: | a Department of Mathematics, Cornell University, 310 Malott Hall, Ithaca, NY 14853-4201, USA b Department of Mathematics, The University of Chicago, 5734 S. University Ave., Chicago, IL 60637-1514, USA |
| |
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. |
| |
Keywords: | Ricci flow Heat equation Li-Yau inequality Harnack inequality Manifold with boundary |
本文献已被 ScienceDirect 等数据库收录! |
|