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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 Dungey. "Some Gradient Estimates on Covering Manifolds." Bulletin of the Polish Academy of Sciences. Mathematics 52.4 (2004): 437-443. <http://eudml.org/doc/280858>.
@article{NickDungey2004, 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.}, author = {Nick Dungey}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, keywords = {heat kernel; Riemannian manifold; covering manifold; gradient estimates; periodic operator; polynomial growth}, language = {eng}, number = {4}, pages = {437-443}, title = {Some Gradient Estimates on Covering Manifolds}, url = {http://eudml.org/doc/280858}, volume = {52}, year = {2004}, }
TY - JOUR AU - Nick Dungey TI - Some Gradient Estimates on Covering Manifolds JO - Bulletin of the Polish Academy of Sciences. Mathematics PY - 2004 VL - 52 IS - 4 SP - 437 EP - 443 AB - 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. LA - eng KW - heat kernel; Riemannian manifold; covering manifold; gradient estimates; periodic operator; polynomial growth UR - http://eudml.org/doc/280858 ER -