##### Department of Mathematics,

University of California San Diego

****************************

### Math 258 - Differential Geometry Seminar

## Sean Curry

#### UCSD

## Strictly pseudoconvex domains in C$^2$ with obstruction flat boundary

##### Abstract:

A bounded strictly pseudoconvex domain in C$^n$, n$>1$, supports a unique complete Kahler-Einstein metric determined by the Cheng-Yau solution of Fefferman's Monge-Ampere equation. The smoothness of the solution of Fefferman's equation up to the boundary is obstructed by a local CR invariant of the boundary called the obstruction density. In the case n=2 the obstruction density is especially important, in particular in describing the logarithmic singularity of the Bergman kernel. For domains in C$^2$ diffeomorphic to the ball, we motivate and consider the problem of determining whether the global vanishing of this obstruction implies biholomorphic equivalence to the unit ball. (This is a strong form of the Ramadanov Conjecture.)

Host: Lei Ni

### November 14, 2018

### 1:00 PM

### AP&M 5829

****************************