How to obtain transience from bounded radial mean curvature

Authors:
Steen Markvorsen and Vicente Palmer

Journal:
Trans. Amer. Math. Soc. **357** (2005), 3459-3479

MSC (2000):
Primary 53C17, 31C12, 60J65

DOI:
https://doi.org/10.1090/S0002-9947-05-03944-9

Published electronically:
April 27, 2005

MathSciNet review:
2146633

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that Brownian motion on any unbounded submanifold in an ambient manifold with a pole is transient if the following conditions are satisfied: The -radial mean curvatures of are sufficiently small outside a compact set and the -radial sectional curvatures of are sufficiently negative. The `sufficiency' conditions are obtained via comparison with explicit transience criteria for radially drifted Brownian motion in warped product model spaces.

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Additional Information

**Steen Markvorsen**

Affiliation:
Department of Mathematics, Technical University of Denmark, DK-2800 Kgs Lyngby, Denmark

Email:
S.Markvorsen@mat.dtu.dk

**Vicente Palmer**

Affiliation:
Departament de Matemàtiques, Universitat Jaume I, 12071 Castellon, Spain

Email:
palmer@mat.uji.es

DOI:
https://doi.org/10.1090/S0002-9947-05-03944-9

Keywords:
Transience,
capacity,
drifted Brownian motion,
submanifolds,
mean curvature,
radial mean curvature,
warped products,
model spaces,
Hadamard--Cartan manifolds,
extrinsic annuli,
comparison theory

Received by editor(s):
October 10, 2003

Published electronically:
April 27, 2005

Additional Notes:
The first author was supported by the Danish Natural Science Research Council

The second author was supported by DGI grant No. BFM2001-3548 and the Danish Natural Science Research Council

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.