Heat trace asymptotics on equiregular sub-Riemannian manifolds

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Abstract

We study a “div-grad type” sub-Laplacian with respect to a smooth measure and its associated heat semigroup on a compact equiregular sub-Riemannian manifold. We prove a short time asymptotic expansion of the heat trace up to any order. Our main result holds true for any smooth measure on the manifold, but it has a spectral geometric meaning when Popp's measure is considered. Our proof is probabilistic. In particular, we use Watanabe's distributional Malliavin calculus.

Original languageEnglish
Pages (from-to)1049-1096
Number of pages48
JournalJournal of the Mathematical Society of Japan
Volume72
Issue number4
DOIs
Publication statusPublished - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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