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Proceedings of the American Mathematical Society

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Brownian functionals on hypersurfaces
in Euclidean space


Authors: Kimberly K. J. Kinateder and Patrick McDonald
Journal: Proc. Amer. Math. Soc. 125 (1997), 1815-1822
MSC (1991): Primary 60J65, 58G32
DOI: https://doi.org/10.1090/S0002-9939-97-03741-6
MathSciNet review: 1371132
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Abstract | References | Similar Articles | Additional Information

Abstract: Using the first exit time for Brownian motion from a smoothly bounded domain in Euclidean space, we define two natural functionals on the space of embedded, compact, oriented, unparametrized hypersurfaces in Euclidean space. We develop explicit formulas for the first variation of each of the functionals and characterize the critical points.


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Additional Information

Kimberly K. J. Kinateder
Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
Address at time of publication: Department of Mathematics, Wright State University, Dayton, Ohio 45435
Email: kjk@euler.math.wright.edu

Patrick McDonald
Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
Address at time of publication: Department of Mathematics, New College of University of South Florida, Sarasota, Florida 34243
Email: pmacdona@virtu.sar.usf.edu, pmacdona@virtu.sar.usf.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03741-6
Keywords: Brownian motion, exit times, variational calculus
Received by editor(s): August 9, 1995
Received by editor(s) in revised form: December 2, 1995
Communicated by: Richard T. Durrett
Article copyright: © Copyright 1997 American Mathematical Society