Revista Matemática Iberoamericana


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Volume 15, Issue 1, 1999, pp. 143–179
DOI: 10.4171/RMI/253

Published online: 1999-04-30

Harnack inequalities on a manifold with positive or negative Ricci curvature

Dominique Bakry[1] and Zhongmin M. Qian[2]

(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. Iberoam. 15 (1999), 143-179. doi: 10.4171/RMI/253