Stochastic completeness and volume growth
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- by Christian Bär and G. Pacelli Bessa PDF
- Proc. Amer. Math. Soc. 138 (2010), 2629-2640 Request permission
Abstract:
It was 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 counterexamples to a converse implication.References
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Additional Information
- Christian Bär
- Affiliation: Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany
- Email: baer@math.uni-potsdam.de
- G. Pacelli Bessa
- Affiliation: Departamento de Matematica, Université Fédérale du Ceará, Bloco 914, Campus do Pici, 60455-760 Fortaleza, Ceará, Brazil
- Email: bessa@mat.ufc.br
- Received by editor(s): August 28, 2009
- Published electronically: March 4, 2010
- Additional Notes: This work was supported by CNPq-CAPES and by Sonderforschungsbereich 647, funded by Deutsche Forschungsgemeinschaft
- Communicated by: Daniel Ruberman
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2629-2640
- MSC (2010): Primary 58J35, 58J65
- DOI: https://doi.org/10.1090/S0002-9939-10-10281-0
- MathSciNet review: 2607893