Hypersurfaces in ℝ^{𝕕} and the variance of exit times for Brownian motion

Kinateder, Kimberly; McDonald, Patrick

doi:10.1090/S0002-9939-97-03925-7

Hypersurfaces in $\mathbb {R}^d$ and the variance of exit times for Brownian motion
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by Kimberly K. J. Kinateder and Patrick McDonald PDF

Proc. Amer. Math. Soc. 125 (1997), 2453-2462 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.

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