A remark on the maximum principle and stochastic completeness

Pigola, Stefano; Rigoli, Marco; Setti, Alberto

doi:10.1090/S0002-9939-02-06672-8

A remark on the maximum principle and stochastic completeness
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by Stefano Pigola, Marco Rigoli and Alberto G. Setti PDF

Proc. Amer. Math. Soc. 131 (2003), 1283-1288 Request permission

Abstract:

We prove that the stochastic completeness of a Riemannian manifold $(M, \langle , \rangle )$ is equivalent to the validity of a weak form of the Omori-Yau maximum principle. Some geometric applications of this result are also presented.

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