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

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.

Cited by in corpus (3)

• On non-visibility of Kobayashi geodesics and the geometry of the boundary
• The Julia-Wolff-Carathéodory theorem in convex finite type domains
• Strong localizations of the Kobayashi distance