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October, 2020 Heat trace asymptotics on equiregular sub-Riemannian manifolds
Yuzuru INAHAMA, Setsuo TANIGUCHI
J. Math. Soc. Japan 72(4): 1049-1096 (October, 2020). DOI: 10.2969/jmsj/82348234

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.

Funding Statement

The first-named author is partially supported by JSPS KAKENHI Grant Number 15K04922, and the second-named author is partially supported by JSPS KAKENHI Grant Number 15K04931.

Citation

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Yuzuru INAHAMA. Setsuo TANIGUCHI. "Heat trace asymptotics on equiregular sub-Riemannian manifolds." J. Math. Soc. Japan 72 (4) 1049 - 1096, October, 2020. https://doi.org/10.2969/jmsj/82348234

Information

Received: 20 March 2019; Published: October, 2020
First available in Project Euclid: 10 September 2020

MathSciNet: MR4165923
Digital Object Identifier: 10.2969/jmsj/82348234

Subjects:
Primary: 53C17
Secondary: 35K08, 41A60, 58J65, 60H07

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 4 • October, 2020
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