Localization of the Kobayashi distance for any visibility domain

Abstract

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

Proposition 3.2, Corollary 3.3 and Remark 3.4 of v2 are combined. The expositions of the proofs of the results are also improved without changing the main idea. 12 pages. To appear in The Journal of Geometric Analysis

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• Strong localizations of the Kobayashi distance