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

 

A remark on the maximum principle and stochastic completeness


Authors: Stefano Pigola, Marco Rigoli and Alberto G. Setti
Journal: Proc. Amer. Math. Soc. 131 (2003), 1283-1288
MSC (2000): Primary 58J35; Secondary 58J65
Published electronically: July 26, 2002
MathSciNet review: 1948121
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Abstract: We prove that the stochastic completeness of a Riemannian manifold $(M, \langle , \rangle)$is equivalent to the validity of a weak form of the Omori-Yau maximum principle. Some geometric applications of this result are also presented.


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Additional Information

Stefano Pigola
Affiliation: Dipartimento di Matematica, Università di Milano, via Saldini 50, I-20133 Milano, Italy
Email: pigola@mat.unimi.it

Marco Rigoli
Affiliation: Dipartimento di Scienze C.F.M., Università dell’Insubria - Como, via Valleggio 11, I-22100 Como, Italy
Email: rigoli@matapp.unimib.it

Alberto G. Setti
Affiliation: Dipartimento di Scienze C.F.M., Università dell’Insubria - Como, via Valleggio 11. I-22100 Como, Italy
Email: setti@uninsubria.it

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06672-8
PII: S 0002-9939(02)06672-8
Keywords: Maximum principle, stochastic completeness
Received by editor(s): January 3, 2001
Received by editor(s) in revised form: November 1, 2001
Published electronically: July 26, 2002
Dedicated: Dedicated to the memory of Franca Burrone Rigoli
Communicated by: Bennett Chow
Article copyright: © Copyright 2002 American Mathematical Society