p-Capacity and p-Hyperbolicity of Submanifolds

Ilkka Holopainen, Steen Markvorsen, Vicente Palmer

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    Abstract

    We use explicit solutions to a drifted Laplace equation in warped product model spaces as comparison constructions to show p-hyperbolicity of a large class of submanifolds for p >= 2. The condition for p-hyperbolicity is expressed in terms of upper support functions for the radial sectional curvatures of the ambient space and for the radial convexity of the submanifold. In the process of showing p-hyperbolicity we also obtain explicit lower bounds on the p-capacity of finite annular domains of the submanifolds in terms of the drifted 2-capacity of the corresponding annuli in the respective comparison spaces.
    Original languageEnglish
    JournalRevista Matemática Iberoamericana
    Volume25
    Issue number2
    Pages (from-to)709-738
    ISSN0213-2230
    Publication statusPublished - 2009

    Keywords

    • p-Transience, p-hyperbolicity
    • Submanifolds
    • Comparison theory

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