Comparison of exit time moment spectra for extrinsic metric balls

Ana Hurtado, Steen Markvorsen, Vicente Palmer

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    Abstract

    We prove explicit upper and lower bounds for the $L^1$-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds $P^m$ in ambient Riemannian spaces $N^n$. We assume that $P$ and $N$ both have controlled radial curvatures (mean curvature and sectional curvature, respectively) as viewed from a pole in $N$. The bounds for the exit moment spectra are given in terms of the corresponding spectra for geodesic metric balls in suitably warped product model spaces. The bounds are sharp in the sense that equalities are obtained in characteristic cases. As a corollary we also obtain new intrinsic comparison results for the exit time spectra for metric balls in the ambient manifolds $N^n$ themselves.
    Original languageEnglish
    JournalPotential Analysis
    Volume36
    Issue number1
    Pages (from-to)137-153
    ISSN0926-2601
    DOIs
    Publication statusPublished - 2012

    Bibliographical note

    Mat-Report No. 2010-01

    Keywords

    • Exit moment spectrum
    • Torsional rigidity
    • Riemannian submanifolds

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