A remark on the maximum principle and stochastic completeness

Stefano Pigola, Marco Rigoli, Alberto G. Setti
2002 Proceedings of the American Mathematical Society  
We prove that the stochastic completeness of a Riemannian manifold (M, , ) is equivalent to the validity of a weak form of the Omori-Yau maximum principle. Some geometric applications of this result are also presented.
doi:10.1090/s0002-9939-02-06672-8 fatcat:l3cmor4uobajpjtzfodft3hxbi