Mean exit time from convex hypersurfaces

Author:
Vicente Palmer

Journal:
Proc. Amer. Math. Soc. **126** (1998), 2089-2094

MSC (1991):
Primary 53C21, 58G32

DOI:
https://doi.org/10.1090/S0002-9939-98-04202-6

MathSciNet review:
1443163

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Abstract | References | Similar Articles | Additional Information

Abstract: L. Karp and M. Pinsky proved that, for small radius , the mean exit time function of an extrinsic -ball in a hypersurface is bounded from below by the corresponding function defined on an extrinsic -ball in . 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.

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Additional Information

**Vicente Palmer**

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

Email:
palmer@mat.uji.es

DOI:
https://doi.org/10.1090/S0002-9939-98-04202-6

Keywords:
Brownian motion,
mean exit time,
convex hypersurface,
extrinsic ball

Received by editor(s):
August 6, 1996

Received by editor(s) in revised form:
December 10, 1996

Additional Notes:
Work partially supported by a DGICYT Grant No. PB94-0972

Communicated by:
Peter Li

Article copyright:
© Copyright 1998
American Mathematical Society