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Some Gradient Estimates on Covering Manifolds

Tom 52 / 2004

Bulletin Polish Acad. Sci. Math. 52 (2004), 437-443 MSC: 58J35, 35B40, 35B27. DOI: 10.4064/ba52-4-10

Streszczenie

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.

Autorzy

• Nick DungeySchool of Mathematics
The University of New South Wales
Sydney 2052, Australia
e-mail

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