Heat content and horizontal mean curvature on the Heisenberg group

Jeremy Tyson, Jing Wang

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)467-505
Number of pages39
JournalCommunications in Partial Differential Equations
Volume43
Issue number3
DOIs
StatePublished - Mar 4 2018

Keywords

  • Brownian motion
  • Heisenberg group
  • heat content
  • horizontal mean curvature
  • horizontal perimeter

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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