Gaussian heat kernel estimates: from functions to forms

2016/06/08 by Coulhon, Thierry, Devyver, Baptiste, Sikora, Adam · 1 citation
#58J35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1606.02423

Abstract

On a complete non-compact Riemannian manifold satisfying the volume doubling property, we give conditions on the negative part of the Ricci curvature that ensure that, unless there are harmonic one-forms, the Gaussian heat kernel upper estimate on functions transfers to one-forms. These conditions do no entail any constraint on the size of the Ricci curvature, only on its decay at infinity.

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• On the Interplay Between Hodge Projections and Bounded Harmonic Functions on Manifolds with Ends

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