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

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2024Embargo end date: 01 Jan 2022 English Publisher:Institute of Mathematics, Polish Academy of SciencesJournal:Annales Polonici Mathematici, volume 132, pages 169-185 (issn: 0066-2216, eissn: 1730-6272, Copyright policy )Funded by:ANR | MINT
Authors: Nikolov, Nikolai; Ökten, Ahmed Yekta; Thomas, Pascal;

doi: 10.4064/ap230522-18-12 , 10.48550/arxiv.2210.10007

arXiv: http://arxiv.org/abs/2210.10007

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.

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Keywords

Mathematics - Complex Variables, Subject Classification. 32F45 Kobayashi distance and Kobayashi-Royden metric, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], Metric Geometry (math.MG), visibility, [MATH] Mathematics [math], localization, Mathematics - Metric Geometry, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], FOS: Mathematics, [MATH]Mathematics [math], Complex Variables (math.CV), geodesics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Top 10%
Average
Average
Green
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