Heat trace asymptotics on equiregular sub-Riemannian manifolds
Differential Geometry
2020-04-15 v3 Probability
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 S. Watanabe's distributional Malliavin calculus.
Keywords
Cite
@article{arxiv.1706.02450,
title = {Heat trace asymptotics on equiregular sub-Riemannian manifolds},
author = {Yuzuru Inahama and Setsuo Taniguchi},
journal= {arXiv preprint arXiv:1706.02450},
year = {2020}
}
Comments
Final version. To appear in J. Math. Soc. Japan. 44 pages. Several minor errors were fixed