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Local and global maxima for the expectation of the lifetime of a Brownian motion on the disk

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Abstract

The quotient of the iterated Green’s function and the Green’s function ∫ D G D (z, ξ)G D (ζ, ξ)dA ξ/G D (z, ζ), which is also called the 3G-expression, plays a fundamental role in potential theory and in the theory of Brownian motion. Recently, Dall’acqua, Grunau and Sweers [5] proved that for the unit disk, the 3G-expression cannot obtain its maximum at interior points. The aim of this paper is to give another proof of this result using only elementary conformal mapping techniques.

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Authors and Affiliations

  1. Naturwissenschaftliche Fakultät III, Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, D06099, Halle (Saale), Germany

    Bodo Dittmar

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  1. Bodo Dittmar
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Correspondence to Bodo Dittmar.

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Dedicated to Reiner Kühnau on the occasion of his 70th birthday

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Dittmar, B. Local and global maxima for the expectation of the lifetime of a Brownian motion on the disk. J Anal Math 104, 59–68 (2008). https://doi.org/10.1007/s11854-008-0016-6

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  • DOI: https://doi.org/10.1007/s11854-008-0016-6

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