Colloquium

In this talk, we shall discuss behavior of the sub-Riemannian geodesics induced by a family of sub-elliptic partial differential equations, especially the sub-Laplacian on a family of pseudo-convex hypersurfaces. In particular, we discuss the complex action function and volume element along the geodesics. Using this action function and the volume element, we obtain the fundamental solution and the heat kernel for the sub-Laplacian. We also try to discuss analysis on decoupled domains in SCV.