Brownian functionals on hypersurfaces in Euclidean space
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- by Kimberly K. J. Kinateder and Patrick McDonald PDF
- Proc. Amer. Math. Soc. 125 (1997), 1815-1822 Request permission
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.References
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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
- Received by editor(s): August 9, 1995
- Received by editor(s) in revised form: December 2, 1995
- Communicated by: Richard T. Durrett
- © Copyright 1997 American Mathematical Society
- 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