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Thierry Delmotte (1999)
Revista Matemática Iberoamericana
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On a graph, we give a characterization of a parabolic Harnack inequality and Gaussian estimates for reversible Markov chains by geometric properties (volume regularity and Poincaré inequality).
Pascal Auscher, Thierry Coulhon (1999)
Annales de l'I.H.P. Probabilités et statistiques
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Robert Kaufman, Jang-Mei Wu (1980)
Compositio Mathematica
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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],...
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.
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.