论文标题
无限的可见性域，最终压实和应用
Unbounded visibility domains, the end compactification, and applications
论文作者
论文摘要
在本文中，我们研究了Kobayashi双曲线结构域上的Kobayashi距离具有一定的可见性特性，重点是无限域。在这种情况下，“可见性”让人联想到可见度，从埃伯林 - 奥尼尔（Eberlein-o'neill）的意义上讲，在呈负弯曲的riemannian流形中可以看出。但是，我们不认为研究的域相对于Kobayashi距离是完整的，因为这很难在$ \ Mathbb {c}^d $，$ d \ geq 2 $中为域中建立。我们研究了该特性控制全态图的边界行为的各种方式。这些结果包括是平面域之间生物形态的carathéodory型延伸定理，尤其是：无限连接的域之间。我们还探索了我们的可见性属性与Kobayashi距离的Gromov双曲线之间的连接。
In this paper we study when the Kobayashi distance on a Kobayashi hyperbolic domain has certain visibility properties, with a focus on unbounded domains. "Visibility" in this context is reminiscent of visibility, seen in negatively curved Riemannian manifolds, in the sense of Eberlein-O'Neill. However, we do not assume that the domains studied are Cauchy-complete with respect to the Kobayashi distance, as this is hard to establish for domains in $\mathbb{C}^d$, $d \geq 2$. We study the various ways in which this property controls the boundary behavior of holomorphic maps. Among these results is a Carathéodory-type extension theorem for biholomorphisms between planar domains, notably: between infinitely-connected domains. We also explore connections between our visibility property and Gromov hyperbolicity of the Kobayashi distance.
