Let M be a complete Riemannian manifold which is a Galois covering, that is, M is periodic under the action of a discrete group G of isometries. Assuming that G has polynomial volume growth, we provide a new proof of Gaussian upper bounds for the gradient of the heat kernel of the Laplace operator on M. Our method also yields a control on the gradient in case G does not have polynomial growth.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-4-10,
author = {Nick Dungey},
title = {Some Gradient Estimates on Covering Manifolds},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {52},
year = {2004},
pages = {437-443},
zbl = {1112.58027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-4-10}
}
Nick Dungey. Some Gradient Estimates on Covering Manifolds. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) pp. 437-443. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-4-10/