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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stochastic completeness and volume growth


Authors: Christian Bär and G. Pacelli Bessa
Journal: Proc. Amer. Math. Soc. 138 (2010), 2629-2640
MSC (2010): Primary 58J35, 58J65
Published electronically: March 4, 2010
MathSciNet review: 2607893
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10281-0
PII: S 0002-9939(10)10281-0
Keywords: Riemannian manifold, Brownian motion, heat kernel, stochastic completeness, volume growth
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.