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

DOI:
https://doi.org/10.1090/S0002-9939-02-06672-8

Published electronically:
July 26, 2002

MathSciNet review:
1948121

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-02-06672-8

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