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Mean exit time from convex hypersurfaces

Authors:	Vicente Palmer

Institution:	Departament de Matematiques, Universitat Jaume I, Castello, Spain

Abstract:	L. Karp and M. Pinsky proved that, for small radius , the mean exit time function $E_{R}$ of an extrinsic -ball in a hypersurface $P^{n-1} \subseteq \mathbb{R}^{n}$ is bounded from below by the corresponding function $\widetilde E_{R}$ defined on an extrinsic -ball in $\mathbb{R}^{n-1}$ . A counterexample given by C. Mueller proves that this inequality doesn't holds in the large. In this paper we show that, if is convex, then the inequality holds for all radii. Moreover, we characterize the equality and show that analogous results are true in the sphere.

Keywords:	Brownian motion mean exit time convex hypersurface extrinsic ball

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