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Heat semigroup on a complete Riemannian manifold. (English) Zbl 0694.58043
Let M be a complete Riemannian manifold and p(t,x,y) the minimal heat kernel on M. Let \(P_ t\) be the associated semigroup. The stochastic completeness \((\int_{M}p(t,x,y)dy=1\), \(t>0)\) and a \(C_ 0\)-diffusion property \((P_ tf\) vanishes at infinity for all \(t>0\) whenever f does) are investigated.
Reviewer: S.Eloshvili

MSC:
58J65 Diffusion processes and stochastic analysis on manifolds
60J60 Diffusion processes
60J65 Brownian motion
58J35 Heat and other parabolic equation methods for PDEs on manifolds
53C20 Global Riemannian geometry, including pinching
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