How to obtain Transience from Bounded Radial Mean Curvature

Steen Markvorsen; Vicente Palmer

doi:10.1090/S0002-9947-05-03944-9

How to obtain Transience from Bounded Radial Mean Curvature

Steen Markvorsen, Vicente Palmer

Jaume I University

Research output: Contribution to journal › Journal article › Research › peer-review

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 outsidea 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.

Original language	English
Journal	Transactions of the American Mathematical Society
Volume	357
Issue number	9
Pages (from-to)	3459-3479
ISSN	0002-9947
DOIs	https://doi.org/10.1090/S0002-9947-05-03944-9
Publication status	Published - 2005

Keywords

transience
capacity
drifted Brownian motion
submanifolds
mean curvature
radial mean curvature
warped products
model spaces
Hadamard-Cartan manifolds
extrinsic annuli

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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 outsidea 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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AB - 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 outsidea 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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KW - capacity

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KW - submanifolds

KW - mean curvature

KW - radial mean curvature

KW - warped products

KW - model spaces

KW - Hadamard-Cartan manifolds

KW - extrinsic annuli

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

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How to obtain Transience from Bounded Radial Mean Curvature

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Keywords

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