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.
Cite this article
Dominique Bakry, Zhongmin M. Qian, Harnack inequalities on a manifold with positive or negative Ricci curvature. Rev. Mat. Iberoam. 15 (1999), no. 1, pp. 143–179DOI 10.4171/RMI/253