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Stochastic completeness and volume growth
Author(s):
Christian
Bär;
G.
Pacelli
Bessa
Journal:
Proc. Amer. Math. Soc.
138
(2010),
2629-2640.
MSC (2010):
Primary 58J35, 58J65
Posted:
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:
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
Posted:
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 of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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