Some Gradient Estimates on Covering Manifolds

Volume 52 / 2004

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


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.


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

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