论文标题
Bergman代表坐标，恒定的全态曲率和Carathéodory定理的多维概括
Bergman representative coordinate, constant holomorphic curvature and a multidimensional generalization of Carathéodory's theorem
论文作者
论文摘要
通过使用Bergman代表坐标和Calabi的分解，我们将LU定理扩展到有界的伪convex结构域，其伯格曼度量与恒定的全态截面曲率不完整。我们将这种域具有生物形态的域特征到可能较小的相对封闭的多极套件。我们还提供了Carathéodory定理的多维概括，内容涉及到封闭的持续扩展。特别是，就伯格曼内核而言，给出了足够的条件，使生物形态球的边界成为拓扑球。
By using the Bergman representative coordinate and Calabi's diastasis, we extend a theorem of Lu to bounded pseudoconvex domains whose Bergman metric is incomplete with constant holomorphic sectional curvature. We characterize such domains that are biholomorphic to a ball possibly less a relatively closed pluripolar set. We also provide a multidimensional generalization of Carathéodory's theorem on the continuous extension of the biholomorphisms up to the closures. In particular, sufficient conditions are given, in terms of the Bergman kernel, for the boundary of a biholomorphic ball to be a topological sphere.
