OFF-DIAGONAL HEAT KERNEL LOWER BOUNDS WITHOUT POINCARÉ 1
On a manifold with polynomial volume growth satisfying Gaussian upper bounds of the heat kernel, a simple characterization of the matching lower bounds is given in terms of a certain Sobolev inequality. The method also works in the case of so-called sub-Gaussian or sub-diffusive heat kernels estimates, which are typical of fractals. Together with previously known results, this yields a new characterization of the full upper and lower Gaussian or sub-Gaussian heat kernel estimates.(Received November 9 2002)
(Revised April 16 2003)
58J35 (primary); 46E35; 47D07 (secondary).
1 Research partially supported by the European Commission (IHP Network ‘Harmonic analysis and related problems’ 2002–2006, contract HPRN-CT-2001-00273-HARP).