Observing integrals of heat kernels from a distance

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    Abstract

    Heat kernels have integrals such as Brownian motion mean exit time, potential capacity, and torsional rigidity. We show how to obtain bounds on these values - essentially by observing their behaviour in terms of the distance function from a point and then comparing with corresponding values in tailor-made warped product spaces. The results will be illustrated by applications to the so-called 'type' problem: How to decide if a given manifold or surface is transient (hyperbolic) or recurrent (parabolic). Specific examples of minimal surfaces and constant pressure dry foams will be shown and discussed as test cases. The talk is based on joint work with Vicente Palmer.
    Original languageEnglish
    Publication date2007
    Publication statusPublished - 2007
    Event11th Danish Center for Applied Mathematics and Mechanics - SAS Radisson Hotel, Silkeborg, Denmark
    Duration: 19 Mar 200721 Mar 2007
    Conference number: 11
    http://www.fam.web.mek.dtu.dk/dcamm05/index.php?navigate=symposia

    Conference

    Conference11th Danish Center for Applied Mathematics and Mechanics
    Number11
    LocationSAS Radisson Hotel
    CountryDenmark
    CitySilkeborg
    Period19/03/200721/03/2007
    Internet address

    Keywords

    • Heat kernels, minimal surfaces, discrete random walks

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