Smoothly bounded domains covering finite volume manifolds
Smoothly bounded domains covering finite volume manifolds
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DOI：
10.4310/jdg/1631124346
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发表时间：
2018-02
影响因子：
2.5
通讯作者：
Andrew M. Zimmer
中科院分区：
文献类型：
--
作者：
Andrew M. Zimmer
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 K\"ahler-Einstein volume, or the Kobayashi-Eisenman volume, then the domain is biholomorphic to the unit ball. This answers an old question of Yau. Further, when the domain is convex we can assume that the boundary only has $C^{1,\epsilon}$ regularity.
