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.
Original language | English (US) |
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Pages (from-to) | 467-505 |
Number of pages | 39 |
Journal | Communications in Partial Differential Equations |
Volume | 43 |
Issue number | 3 |
DOIs | |
State | Published - Mar 4 2018 |
Keywords
- Brownian motion
- Heisenberg group
- heat content
- horizontal mean curvature
- horizontal perimeter
ASJC Scopus subject areas
- Analysis
- Applied Mathematics