A remark on the maximum principle and stochastic completeness
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- by Stefano Pigola, Marco Rigoli and Alberto G. Setti
- Proc. Amer. Math. Soc. 131 (2003), 1283-1288
- DOI: https://doi.org/10.1090/S0002-9939-02-06672-8
- Published electronically: July 26, 2002
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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.References
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Bibliographic Information
- Stefano Pigola
- Affiliation: Dipartimento di Matematica, Università di Milano, via Saldini 50, I-20133 Milano, Italy
- MR Author ID: 701188
- 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
- MR Author ID: 148315
- 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
- MR Author ID: 289546
- Email: setti@uninsubria.it
- Received by editor(s): January 3, 2001
- Received by editor(s) in revised form: November 1, 2001
- Published electronically: July 26, 2002
- Communicated by: Bennett Chow
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1283-1288
- MSC (2000): Primary 58J35; Secondary 58J65
- DOI: https://doi.org/10.1090/S0002-9939-02-06672-8
- MathSciNet review: 1948121
Dedicated: Dedicated to the memory of Franca Burrone Rigoli