Heat trace asymptotics on equiregular sub-Riemannian manifolds

Yuzuru Inahama; Setsuo Taniguchi

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arXiv · 1706.02450

Heat trace asymptotics on equiregular sub-Riemannian manifolds

Yuzuru Inahama·Setsuo Taniguchi

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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 S. Watanabe's distributional Malliavin calculus.

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Yuzuru Inahama, Setsuo Taniguchi. 2017-06-08. Heat trace asymptotics on equiregular sub-Riemannian manifolds. https://arxiv.org/abs/1706.02450

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