Local and global notions of visibility with respect to Kobayashi distance, a comparison

TL;DR

This paper introduces the concept of visible boundary points relative to Kobayashi distance in complex domains, establishing localization results and demonstrating that visibility is a local boundary property independent of the domain.

Contribution

It defines visible boundary points for Kobayashi distance and proves localization results, showing that visibility is a local boundary property unaffected by the domain.

Findings

Visibility property is local and domain-independent.

Localization results for Kobayashi distance near boundary points.

Visibility can be characterized using additive and multiplicative localization.

Abstract

In this note, we introduce the notion of visible boundary points with respect to Kobayashi distance for domains in complex euclidean space. Following the work of Sarkar, we obtain additive and multiplicative localization results about Kobayashi distance near visible boundary points. Then using the additive localization result, we show that visibility property with respect to Kobayashi distance is a local property of the boundary points and it does not depend on the domain.