Localization of the Kobayashi distance for any visibility domain

TL;DR

This paper establishes localization results for the Kobayashi distance in visibility domains in complex spaces, advancing understanding of hyperbolic geometry in several complex variables.

Contribution

It introduces localization results for the Kobayashi distance and Kobayashi-Royden pseudometric in visibility domains, extending previous geometric analysis methods.

Findings

Localization of Kobayashi distance in visibility domains

Localization of Kobayashi-Royden pseudometric

Results applicable to complex spaces of dimension d ≥ 1

Abstract

In this article, we prove localization results for the Kobayashi distance of Kobayashi hyperbolic domains with local visibility property in $\mathbb{C}^d$, $d \geq 1$. This is done by proving a localization result for the Kobayashi-Royden pseudometric, along with some other results for domains satisfying local weak visibility.