Mathematics – Differential Geometry
Scientific paper
2009-08-28
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.
Baer Christian
Bessa Gregorio Pacelli
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