Some Gradient Estimates on Covering Manifolds
Volume 52 / 2004
Bulletin Polish Acad. Sci. Math. 52 (2004), 437-443
MSC: 58J35, 35B40, 35B27.
DOI: 10.4064/ba52-4-10
Abstract
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.
