Small time Gaussian estimates of heat diffusion kernels. I: The semigroup technique. (English) Zbl 0703.58052

The author gives Gaussian bounds for the heat kernel of the Laplace- Beltrami operator on a Riemannian manifold with Ricci curvature bounded from below by a negative constant. In particular the author gives new (small time) upper estimates as well as bounds for the time derivatives of the kernel.
Further the author gives interesting results for certain subelliptic operators of second order. In particular a Harnack-type estimate is mentioned as well as upper bounds for the heat kernel associated with such an operator are given.
Reviewer: N.Jacob


58J35 Heat and other parabolic equation methods for PDEs on manifolds
35K05 Heat equation
60H99 Stochastic analysis