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September 2021 Smoothly bounded domains covering finite volume manifolds
Andrew Zimmer
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J. Differential Geom. 119(1): 161-182 (September 2021). DOI: 10.4310/jdg/1631124346

Abstract

In this paper we prove: if a bounded domain with $C^2$ boundary covers a manifold which has finite volume with respect to either the Bergman volume, the Kähler–Einstein volume, or the Kobayashi–Eisenman volume, then the domain is biholomorphic to the unit ball. This answers a question attributed to Yau. Further, when the domain is convex we can assume that the boundary only has $C^{1,\epsilon}$ regularity.

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Andrew Zimmer. "Smoothly bounded domains covering finite volume manifolds." J. Differential Geom. 119 (1) 161 - 182, September 2021. https://doi.org/10.4310/jdg/1631124346

Information

Received: 12 March 2018; Accepted: 19 September 2019; Published: September 2021
First available in Project Euclid: 10 September 2021

Digital Object Identifier: 10.4310/jdg/1631124346

Keywords: Bergman metric , biholomorphism group , finite volume complex manifolds , Kähler–Einstein metric , Kobayashi metric , rigidity

Rights: Copyright © 2021 Lehigh University

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Vol.119 • No. 1 • September 2021
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