Large time behaviour of heat kernels on non-compact manifolds: fast and slow decays
Thierry Coulhon (1998)
Journées équations aux dérivées partielles
Similarity:
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....