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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have