Sharp heat kernel bounds for some Laplace operators. (English) Zbl 0701.35004
The authors improve an upper bound for the heat kernel of a complete Riemann manifold M, given by the first author in an earlier paper. The better estimate is obtained if one assumes that -\(\Delta\) (\(\Delta\) is the Laplace-Beltrami operator on M) satisfies a logarithmic Sobolev inequality.
Reviewer: C.Popa
MSC:
35A08 | Fundamental solutions to PDEs |
58J35 | Heat and other parabolic equation methods for PDEs on manifolds |
35C15 | Integral representations of solutions to PDEs |