Hypersurfaces in ![]() and the variance of exit times for Brownian motion |
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| Authors: | Kimberly K. J. Kinateder Patrick McDonald |
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| Affiliation: | Department of Mathematics and Statistics, Wright State University, Dayton, Ohio 45435-0001 ; Department of Mathematics, University of South Florida, Sarasota, Florida |
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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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| Keywords: | Brownian motion exit times variance variational calculus free boundary problems |
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