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 pre- sented.
Pigola, S., Rigoli, M., Setti, A. (2003). A remark on the maximum principle and stochastic completeness. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 131(4), 1283-1288 [10.1090/S0002-9939-02-06672-8].
A remark on the maximum principle and stochastic completeness
PIGOLA, STEFANO;
2003
Abstract
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 pre- sented.
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