title: Heat kernel asymptotic expansions for the Heisenberg sub-Laplacian and the Grushin operator.
abstract: The sub-Laplacian on the Heisenberg group and the Grushin operator are typical examples of sub-elliptic operators. Their heat kernels are both given in the form of Laplace-type integrals. By using Laplace's method, the method of stationary phase and the method of steepest descent, we derive the small-time asymptotic expansions for these heat kernels, which are related to the geodesic structure of the induced geometries.
authors: Department of Mathematics and Department of Computer Sciences , Georgetown University , Washington, DC 20057, USA ; Department of Mathematics , Fu Jen Catholic University , Taipei 242, Taiwan, Republic of China.
authors: Der-Chen
authors: C
authors: Chang
authors: Department of Mathematics, and Institute for Computational and Theoretical Studies , Hong Kong Baptist University , Kowloon, Hong Kong.
authors: Yutian
authors: 0000-0003-1810-3000
authors: Y
authors: Li
keywords: Grushin operator; Heisenberg group; asymptotic expansions; heat kernel; saddle point method; small-time asymptotics