A concrete approach to diagonal short time asymptotics of heat kernels associated with sub-Laplacian on CR manifolds

TL;DR

This paper constructs a diffusion process on CR manifolds and analyzes the short-time behavior of its heat kernel, revealing connections between the asymptotics and the underlying geometric structure.

Contribution

It provides a concrete method to derive the diagonal short-time asymptotics of heat kernels associated with the sub-Laplacian on CR manifolds using Watanabe's expansion.

Findings

Derived explicit asymptotic expansion for heat kernels

Established relationship between asymptotics and CR geometry

Enhanced understanding of heat kernel behavior on CR manifolds

Abstract

A diffusion process associated with the real sub-Laplacian $\Delta_b$, the real part of the complex Kohn-Spencer Laplacian $\square_b$, on a strictly pseudoconvex CR manifold has been constructed. In this paper, we investigate diagonal short time asymptotics of the heat kernel corresponding to the diffusion process by using Watanabe's asymptotic expansion and give a representation for the asymptotic expansion of heat kernels which shows a relationship to the geometric structure.