TY - JOUR
T1 - Heat trace asymptotics on equiregular sub-Riemannian manifolds
AU - Inahama, Yuzuru
AU - Taniguchi, Setsuo
N1 - Funding Information:
2010 Mathematics Subject Classification. Primary 53C17; Secondary 60H07, 58J65, 35K08, 41A60. Key Words and Phrases. sub-Riemannian geometry, heat kernel, stochastic differential equation, Malliavin calculus, asymptotic expansion. 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.
Publisher Copyright:
© 2020 The Mathematical Society of Japan
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
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U2 - 10.2969/jmsj/82348234
DO - 10.2969/jmsj/82348234
M3 - Article
AN - SCOPUS:85096235636
SN - 0025-5645
VL - 72
SP - 1049
EP - 1096
JO - Journal of the Mathematical Society of Japan
JF - Journal of the Mathematical Society of Japan
IS - 4
ER -