How to obtain Transience from Bounded Radial Mean Curvature

Steen Markvorsen, Vicente Palmer

    Research output: Contribution to journalJournal articleResearchpeer-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 languageEnglish
    JournalTransactions of the American Mathematical Society
    Volume357
    Issue number9
    Pages (from-to)3459-3479
    ISSN0002-9947
    DOIs
    Publication statusPublished - 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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