##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry Seminar

## Andrew Zimmer

#### University of Wisconsin- Madison

## Analytic problems on domains with good intrinsic geometry

##### Abstract:

In this talk, I will describe a new class of domains in complex Euclidean space which is defined in terms of the existence of Kaehler metrics with good geometric properties. By definition, this class is invariant under biholomorphism. It also includes many well-studied classes of domains such as strongly pseudoconvex domains, finite type domains in dimension two, convex domains, homogeneous domains, and embeddings of Teichmuller space. Analytic problems are also tractable for this class, in particular we show that compactness of the dbar-Neumann operator on (0,q)-forms is equivalent to a growth condition of the Bergman metric. This generalizes an old result of Fu-Straube for convex domains.

Host: Lei Ni

### April 7, 2021

### 11:00 AM

### Zoom ID 917 6172 6136

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