Localization of the Kobayashi distance for any visibility domain

Amar Deep Sarkar

Localization of the Kobayashi distance for any visibility domain

Complex Variables 2023-01-25 v3

Authors: Amar Deep Sarkar

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.

Keywords

kobayashi distance kobayashi-royden pseudometric visibility domain localization complex analysis

Cite

@article{arxiv.2209.07782,
  title  = {Localization of the Kobayashi distance for any visibility domain},
  author = {Amar Deep Sarkar},
  journal= {arXiv preprint arXiv:2209.07782},
  year   = {2023}
}

Comments

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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