Harnack inequalities on a manifold with positive or negative Ricci curvature
Open Access
- 30 April 1999
- journal article
- Published by European Mathematical Society - EMS - Publishing House GmbH in Revista Matemática Iberoamericana
- Vol. 15 (1) , 143-179
Abstract
Several new Harnack estimates for positive solutions of the heat equation on a complete Riemannian manifold with Ricci curvature bounded below by a positive or a negative constant are established. These estimates are sharp both for small time for large time and for large distance and lead to new estimates for the heat kernel of a manifold with Ricci curvature bounded below.Keywords
This publication has 5 references indexed in Scilit:
- On Harnack estimates for positive solutions of the heat equation on a complete manifoldComptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1997
- Matrix Harnack estimate for the heat equationCommunications in Analysis and Geometry, 1993
- Heat kernel bounds on manifoldsMathematische Annalen, 1992
- A lower bound for the heat kernelCommunications on Pure and Applied Mathematics, 1981
- Harmonic functions on complete riemannian manifoldsCommunications on Pure and Applied Mathematics, 1975