Displaying similar documents to “On the relation between elliptic and parabolic Harnack inequalities”

Heat kernel upper bounds on a complete non-compact manifold.

Alexander Grigor'yan (1994)

Revista Matemática Iberoamericana

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Let M be a smooth connected non-compact geodesically complete Riemannian manifold, Δ denote the Laplace operator associated with the Riemannian metric, n ≥ 2 be the dimension of M. Consider the heat equation on the manifold ut - Δu = 0, where u = u(x,t), x ∈ M, t > 0. The heat kernel p(x,y,t) is by definition the smallest positive fundamental solution to the heat equation which exists on any manifold (see [Ch],...

Heat kernel on manifolds with ends

Alexander Grigor’yan, Laurent Saloff-Coste (2009)

Annales de l’institut Fourier

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We prove two-sided estimates of heat kernels on non-parabolic Riemannian manifolds with ends, assuming that the heat kernel on each end separately satisfies the Li-Yau estimate.

Harnack inequalities on a manifold with positive or negative Ricci curvature.

Dominique Bakry, Zhongmin M. Qian (1999)

Revista Matemática Iberoamericana

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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.