Stochastic completeness and volume growth

Details Stochastic completeness and volume growth Stochastic completeness and volume growth

2009-08-28

arxiv.org/abs/0908.4222v2

Proc. Amer. Math. Soc. 138 (2010), 2629-2640

Mathematics

Differential Geometry

11 pages, 5 figures, published version

Scientific paper

10.1090/S0002-9939-10-10281-0

It has been suggested in 1999 that a certain volume growth condition for geodesically complete Riemannian manifolds might imply that the manifold is stochastically complete. This is motivated by a large class of examples and by a known analogous criterion for recurrence of Brownian motion. We show that the suggested implication is not true in general. We also give counter-examples to a converse implication.

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