Transience and capacity of minimal submanifolds

Steen Markvorsen, V. Palmer

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    We prove explicit lower bounds for the capacity of annular domains of minimal submanifolds P-m in ambient Riemannian spaces N-n with sectional curvatures bounded from above. We characterize the situations in which the lower bounds for the capacity are actually attained. Furthermore we apply these bounds to prove that Brownian motion defined on a complete minimal submanifold is transient when the ambient space is a negatively curved Hadamard-Cartan manifold. The proof stems directly from the capacity bounds and also covers the case of minimal submanifolds of dimension m > 2 in Euclidean spaces.
    Original languageEnglish
    JournalGeometric and Functional Analysis
    Volume13
    Issue number4
    Pages (from-to)915-933
    ISSN1016-443X
    DOIs
    Publication statusPublished - 2003

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