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Alexander Grigor'yan; Laurent Saloff-Coste
Stability results for Harnack inequalities
(Résultats de stabilité pour les inégalités de Harnack)
Annales de l'institut Fourier, 55 no. 3 (2005), p. 825-890, doi: 10.5802/aif.2116
Article PDF | Reviews MR 2149405 | Zbl 02171527 | 2 citations in Cedram
Class. Math.: 58J35, 31C12
Keywords: Harnack inequality, Riemannian manifold, heat equation

Résumé - Abstract

We develop new techniques for proving uniform elliptic and parabolic Harnack inequalities on weighted Riemannian manifolds. In particular, we prove the stability of the Harnack inequalities under certain non-uniform changes of the weight. We also prove necessary and sufficient conditions for the Harnack inequalities to hold on complete non-compact manifolds having non-negative Ricci curvature outside a compact set and a finite first Betti number or just having asymptotically non-negative sectional curvature.

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