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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 $P$ in an ambient manifold $N$ with a pole $p$ is transient if the following conditions are satisfied: The $p$-radial mean curvatures of $P$ are sufficiently small outside a compact set and the $p$-radial sectional curvatures of $N$ 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.

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