摘  要:

The Grauert tube  of a real analytic manifold  is a strongly pseudoconvex domain whose defining function is derived from the Riemannian metric . In fact,  is diffeomorphic to the co-ball bundle  under the complexified exponential map. Grauert tubes therefore offer a bridge between the setting of geometric quantization (where the dual circle bundle is a strongly pseudoconvex domain) and the setting of standard quantization on Riemannian manifold.

In this talk, I will focus on analysis on Grauert tubes and present a recent joint work with Abe Rabinowitz (Northwestern University) on near-diagonal scaling asymptotics for the Szego kernel. As an application, we obtain sharp  norm estimates on complexified Laplace eigenfunctions (Husimi distributions).