How to obtain transience from bounded radial mean curvature

Markvorsen, Steen; Palmer, Vicente

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

How to obtain transience from bounded radial mean curvature
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by Steen Markvorsen and Vicente Palmer

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

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

Published electronically: April 27, 2005

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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 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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