Large time behaviour of heat kernels on non-compact manifolds : fast and slow decays
Coulhon, Thierry
Journées équations aux dérivées partielles, (1998), p. 1-12 / Harvested from Numdam
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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 L 2 isoperimetric profile. The main point is to connect the decay of the L 1 -L ∞ 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?

Publié le : 1998-01-01
@article{JEDP_1998____A2_0,
     author = {Coulhon, Thierry},
     title = {Large time behaviour of heat kernels on non-compact manifolds : fast and slow decays},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {1998},
     pages = {1-12},
     zbl = {01808712},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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), pp. 1-12. http://gdmltest.u-ga.fr/item/JEDP_1998____A2_0/

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