| 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.
(This is a jointwork with Setsuo Taniguchi.) |
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