Revista Matemática Iberoamericana
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Published online: 1999-04-30
Harnack inequalities on a manifold with positive or negative Ricci curvatureDominique Bakry and Zhongmin M. Qian (1) Université Paul Sabatier, Toulouse, France
(2) Imperial College, London, UK
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.
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Bakry Dominique, Qian Zhongmin: Harnack inequalities on a manifold with positive or negative Ricci curvature. Rev. Mat. Iberoamericana 15 (1999), 143-179. doi: 10.4171/RMI/253