论文标题
Kobayashi指标和应用的本地化
Localization of the Kobayashi metric and applications
论文作者
论文摘要
在本文中，我们介绍了一个新的域 - log-type凸域，这些域没有边界规则性假设。然后，我们将在log-type凸子域中将Kobayashi度量定位。作为应用程序，我们证明了具有log型凸dini-smooth边界点的两个有界域之间的粗略等距图连续扩展的本地版本。此外，我们证明TeichMüller空间$ \ MATHCAL t_ {g，n} $对$ \ MATHBB C^{3G-3+n} $中的任何有限的Pseudoconvex域都不是生物形态，这是本地log-type type convex近边界点附近的局部log-type convex。
In this paper we introduce a new class of domains -- log-type convex domains, which have no boundary regularity assumptions. Then we will localize the Kobayashi metric in log-type convex subdomains. As an application, we prove a local version of continuous extension of rough isometric maps between two bounded domains with log-type convex Dini-smooth boundary points. Moreover we prove that the Teichmüller space $\mathcal T_{g,n}$ is not biholomorphic to any bounded pseudoconvex domain in $\mathbb C^{3g-3+n}$ which is locally log-type convex near some boundary point.
