In this talk we shall present some joint work with A. Grigory’an. Upper and lower estimates on the rate of decay of the heat kernel on a complete non-compact riemannian manifold have recently been obtained in terms of the geometry at infinity of the manifold, more precisely in terms of a kind of isoperimetric profile. The main point is to connect the decay of the norm of the heat semigroup with some adapted Nash or Faber-Krahn inequalities, which is done by functional analytic methods. We shall give an outline of these results and show how they can give some answers to the following question: given the volume growth of a manifold, e.g. polynomial or exponential, how fast and how slow can the heat kernel decay be?
@incollection{JEDP_1998____A2_0, author = {Thierry Coulhon}, title = {Large time behaviour of heat kernels on non-compact manifolds : fast and slow decays}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {2}, pages = {1--12}, publisher = {Universit\'e de Nantes}, year = {1998}, zbl = {01808712}, language = {en}, url = {https://proceedings.centre-mersenne.org/item/JEDP_1998____A2_0/} }
TY - JOUR AU - Thierry Coulhon TI - Large time behaviour of heat kernels on non-compact manifolds : fast and slow decays JO - Journées équations aux dérivées partielles PY - 1998 SP - 1 EP - 12 PB - Université de Nantes UR - https://proceedings.centre-mersenne.org/item/JEDP_1998____A2_0/ LA - en ID - JEDP_1998____A2_0 ER -
%0 Journal Article %A Thierry Coulhon %T Large time behaviour of heat kernels on non-compact manifolds : fast and slow decays %J Journées équations aux dérivées partielles %D 1998 %P 1-12 %I Université de Nantes %U https://proceedings.centre-mersenne.org/item/JEDP_1998____A2_0/ %G en %F JEDP_1998____A2_0
Thierry Coulhon. Large time behaviour of heat kernels on non-compact manifolds : fast and slow decays. Journées équations aux dérivées partielles (1998), article no. 2, 12 p. https://proceedings.centre-mersenne.org/item/JEDP_1998____A2_0/
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