##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry

## Ming Xiao

#### UCSD

## Bergman-Einstein metrics on strongly pseudoconvex domains

##### Abstract:

We explain a recent work with Huang where we combine various results in complex analysis including Fefferman's invariant theory, the Chern-Moser theory, the Cheng-Yau solution of Kahler-Einstein metrics, to provide an affirmative solution of a conjecture posed by Cheng-Yau. The conjecture stated that the Bergman metric of a bounded strongly pseudoconvex domain is Einstein if and only if the domain is holomorphically equivalent to the ball.

Host: Lei Ni

### February 14, 2018

### 1:00 PM

### AP&M 7321

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