##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry

## Feng Luo

#### Rutgers University

## Koebe circle domain conjecture and the Weyl problem in hyperbolic 3-space

##### Abstract:

In 1908, Paul Koebe conjectured that every open connected set in the plane is conformally diffeomorphic to an open connected set whose boundary components are either round circles or points. The Weyl problem, in the hyperbolic setting, asks for isometric embedding of surfaces of curvature at least -1 in to the hyperbolic 3-space. We show that there are close relationships among the Koebe conjecture, the Weyl problem and the work of Alexandrov and Thurston on convex surfaces. This is a joint work with Tianqi Wu.

Host: Ben Chow

### April 24, 2019

### 2:00 PM

### AP&M 5829

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