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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 = {Coulhon, Thierry},
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},
doi = {10.5802/jedp.531},
zbl = {01808712},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5802/jedp.531/}
}
TY - JOUR AU - Coulhon, Thierry 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 - http://geodesic.mathdoc.fr/articles/10.5802/jedp.531/ DO - 10.5802/jedp.531 LA - en ID - JEDP_1998____A2_0 ER -
%0 Journal Article %A Coulhon, Thierry %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 http://geodesic.mathdoc.fr/articles/10.5802/jedp.531/ %R 10.5802/jedp.531 %G en %F JEDP_1998____A2_0
Coulhon, Thierry. 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.. doi: 10.5802/jedp.531
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