Heat trace asymptotics on equiregular sub-Riemannian manifolds

被引：1

作者：

Inahama, Yuzuru ^{[1
]}

Taniguchi, Setsuo ^{[2
]}

机构：

[1] Kyushu Univ, Fac Math, Nishi Ku, Motooka 744, Fukuoka 8190395, Japan

[2] Kyushu Univ, Fac Arts & Sci, Nishi Ku, Motooka 744, Fukuoka 8190395, Japan

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2020年 / 72卷 / 04期

关键词：

sub-Riemannian geometry; heat kernel; stochastic differential equation; Malliavin calculus; asymptotic expansion; SPECTRAL ZETA-FUNCTION; EXPONENTIAL DECAY; TIME ASYMPTOTICS; LAPLACIAN; INTEGRALS; OPERATORS; KERNELS;

D O I：

10.2969/jmsj/82348234

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1049 / 1096

页数：48

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