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Heat kernel bounds, conservation of probability and the Feller property. (English) Zbl 0808.58041
The author studies conditions under which the heat semigroup of a weighted Laplace-Beltrami operator on a Riemannian manifold conserves probability and has the Feller property, respectively. He obtains a pointwise Gaussian upper bound on heat kernels. The results can be extended for instance to Lipschitz manifolds.
Reviewer: H.Baum (Berlin)

MSC:
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
35P20 Asymptotic distributions of eigenvalues in context of PDEs
53C12 Foliations (differential geometric aspects)
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