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arXiv · 1706.01477

Heat content and horizontal mean curvature on the Heisenberg group

Jeremy Tyson·Jing Wang
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Abstract

We identify the short time asymptotics of the sub-Riemannian heat content for a smoothly bounded domain in the first Heisenberg group. Our asymptotic formula generalizes prior work by van den Berg-Le Gall and van den Berg-Gilkey to the sub-Riemannian context, and identifies the first few coefficients in the sub-Riemannian heat content in terms of the horizontal perimeter and the total horizontal mean curvature of the boundary. The proof is probabilistic, and relies on a characterization of the heat content in terms of Brownian motion.

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Jeremy Tyson, Jing Wang. 2017-06-05. Heat content and horizontal mean curvature on the Heisenberg group. https://doi.org/10.1080/03605302.2018.1446166

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