Bergman–Einstein metrics, a generalization of Kerner’s theorem and Stein spaces with spherical boundaries
Bergman–Einstein metrics, a generalization of Kerner’s theorem and Stein spaces with spherical boundaries
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DOI：
10.1515/crelle-2020-0012
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发表时间：
2020-05
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影响因子：
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通讯作者：
Xiaojun Huang;Ming Xiao
中科院分区：
文献类型：
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作者：
Xiaojun Huang;Ming Xiao
本文给出了Cheng在1979年提出的一个猜想的肯定解，该猜想断言n ∈ N，n ≥ 2 {\mathbb{C}^{n}，n\geq 2}中光滑有界强伪凸域的Bergman度量是Kähler-Einstein当且仅当该域与球双全纯.我们建立了一个版本的经典Kerner定理的Stein空间与孤立的奇点，它有一个直接的应用，以构建一个双曲度量的Stein空间与球面边界。
Abstract We give an affirmative solution to a conjecture of Cheng proposed in 1979 which asserts that the Bergman metric of a smoothly bounded strongly pseudoconvex domain in ℂ n , n ≥ 2 {\mathbb{C}^{n},n\geq 2} , is Kähler–Einstein if and only if the domain is biholomorphic to the ball. We establish a version of the classical Kerner theorem for Stein spaces with isolated singularities which has an immediate application to construct a hyperbolic metric over a Stein space with a spherical boundary.