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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)
##### Keywords:
heat kernel; Laplacian; Riemannian manifold; Feller property
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##### References:
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