Stability results for Harnack inequalities
Annales de l'Institut Fourier, Volume 55 (2005) no. 3, pp. 825-890.

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.

Nous développons de nouvelles techniques pour obtenir des inégalités de Harnack uniformes elliptiques et paraboliques sur les variétés riemanniennes à poids. Nous démontrons en particulier la stabilité de ces inégalités pour certains changements de poids. Nous donnons une condition nécessaire et suffisante pour ces inégalités dans le cas des variétés riemanniennes complètes à courbure de Ricci positive ou nulle en dehors d’un compact et dont le premier nombre de Betti est fini, ou sous la condition de courbure sectionnelle asymptotiquement positive ou nulle.

DOI: 10.5802/aif.2116
Classification: 58J35,  31C12
Keywords: Harnack inequality, Riemannian manifold, heat equation
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Grigor'yan, Alexander; Saloff-Coste, Laurent. Stability results for Harnack inequalities. Annales de l'Institut Fourier, Volume 55 (2005) no. 3, pp. 825-890. doi : 10.5802/aif.2116. https://aif.centre-mersenne.org/articles/10.5802/aif.2116/

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