Heat trace asymptotics on equiregular sub-Riemannian manifolds
arXiv:1706.02450
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.
Final version. To appear in J. Math. Soc. Japan. 44 pages. Several minor errors were fixed