Stochastic completeness and volume growth

Autoren: Christian Bär, Gregorio Pacelli Bessa (2010)

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.

Zeitschrift:
Proc. Amer. Math. Soc.
Verlag:
American Mathematical Society
Seiten:
2629-2640
Band:
138, no. 7

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