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A remark on the maximum principle and stochastic completeness
Author(s):
Stefano
Pigola;
Marco
Rigoli;
Alberto
G.
Setti
Journal:
Proc. Amer. Math. Soc.
131
(2003),
1283-1288.
MSC (2000):
Primary 58J35;
Secondary 58J65
Posted:
July 26, 2002
MathSciNet review:
1948121
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Abstract:
We prove that the stochastic completeness of a Riemannian manifold  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:
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
Posted:
July 26, 2002
Dedicated:
Dedicated to the memory of Franca Burrone Rigoli
Communicated by:
Bennett Chow
Copyright of article:
Copyright
2002,
American Mathematical Society
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