Xin Dong -- Bergman-Calabi diastasis and Kahler metric of constant holomorphic sectional curvature.
Author information
- Xin Dong
- University of Connecticut
- Website: https://sites.google.com/site/1987xindong/
Abstract:
With Bun Wong at UC Riverside, we study bounded domains in \(\mathbb C^n\) with the Bergman metric of constant holomorphic sectional curvature. We give equivalent conditions for the domains being biholomorphic to a ball in terms of the exhaustiveness of the Bergman-Calabi diastasis. In particular, we prove that such domains are Lu Qi-Keng. We also extend a theorem of Lu towards the incomplete situation and characterize pseudoconvex domains that are biholomorphic to a ball possibly less a relatively closed pluripolar set. Time permitting, I will mention some applications to Riemann surfaces.