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