Hsu, Pei Heat semigroup on a complete Riemannian manifold. (English) Zbl 0694.58043 Ann. Probab. 17, No. 3, 1248-1254 (1989). 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 Cited in 39 Documents 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 Keywords:Brownian motion; Riemannian manifold; \(C_ 0\)-diffusion PDFBibTeX XMLCite \textit{P. Hsu}, Ann. Probab. 17, No. 3, 1248--1254 (1989; Zbl 0694.58043) Full Text: DOI