154 Hurley Hall
In this talk, we study small time asymptotic of the heat content for a smoothly bounded domain in the Heisenberg group, which captures geometric information of the boundary including perimeter and the total horizontal mean curvature of the boundary of the domain.
We use probabilistic method by studying the escaping probability of the horizontal Brownian motion process that is canonically associated to the sub-Riemannian (degenerate) structure of the Heisenberg group.
This is a joint work with J. Tyson.
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