分野別セミナー

Abstract:
We construct 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 via the method of Eells, Elworthy and Malliavin by taking advantage of the metric connection due to Tanaka and Webster.

Using the diffusion process and the Malliavin calculus, we study the Dirichlet problem for $\Delta_b$ are studied in a probabilistic manner and investigate distributions of stochastic line integrals along the diffusion process. Moreover,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.