覆盖有限体积流形的光滑有界域

IF 1.3 1区数学 Q1 MATHEMATICS

Journal of Differential Geometry Pub Date : 2018-02-04 DOI:10.4310/jdg/1631124346

Andrew M. Zimmer

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引用次数: 4

摘要

本文证明:如果一个边界为C^2的有界区域覆盖了一个体积有限的流形，无论该流形是相对于Bergman体积、K\ ahler-Einstein体积还是Kobayashi-Eisenman体积，那么该区域对单位球是生物全纯的。这回答了你的一个老问题。更进一步，当定义域是凸的时候，我们可以假设边界只有C^{1，\epsilon}$正则性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Smoothly bounded domains covering finite volume manifolds

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.

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来源期刊

Journal of Differential Geometry 数学-数学

CiteScore

3.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes the latest research in differential geometry and related areas of differential equations, mathematical physics, algebraic geometry, and geometric topology.