Gaussian heat kernel estimates: from functions to forms
Analysis of PDEs
2016-06-09 v1
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.
Cite
@article{arxiv.1606.02423,
title = {Gaussian heat kernel estimates: from functions to forms},
author = {Thierry Coulhon and Baptiste Devyver and Adam Sikora},
journal= {arXiv preprint arXiv:1606.02423},
year = {2016}
}