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Brownian functionals on hypersurfaces in Euclidean space
Author(s):
Kimberly
K. J.
Kinateder;
Patrick
McDonald
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1815-1822.
MSC (1991):
Primary 60J65, 58G32
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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:
10.1090/S0002-9939-97-03741-6
PII:
S 0002-9939(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
Copyright of article:
Copyright
1997,
American Mathematical Society
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