JournalsrmiVol. 15, No. 1pp. 143–179

Harnack inequalities on a manifold with positive or negative Ricci curvature

  • Dominique Bakry

    Université Paul Sabatier, Toulouse, France
  • Zhongmin M. Qian

    Imperial College, London, UK
Harnack inequalities on a manifold with positive or negative Ricci curvature cover
Download PDF

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.

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. 143–179

DOI 10.4171/RMI/253