Quasicircles and width of Jordan curves in CP1
| Autor: | Jean-Marc Schlenker, Francesco Bonsante, Jeffrey Danciger, Sara Maloni |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Mathematics::Complex Variables
General Mathematics 010102 general mathematics 0103 physical sciences Mathematics::Rings and Algebras Mathematics [G03] [Physical chemical mathematical & earth Sciences] Geometry 010307 mathematical physics Mathématiques [G03] [Physique chimie mathématiques & sciences de la terre] 0101 mathematics 01 natural sciences Mathematics |
| Popis: | We study a notion of "width" for Jordan curves in CP1, paying special attention to the class of quasicircles. The width of a Jordan curve is defined in terms of the geometry of its convex hull in hyperbolic three-space. A similar invariant in the setting of anti de Sitter geometry was used by Bonsante-Schlenker to characterize quasicircles amongst a larger class of Jordan curves in the boundary of anti de Sitter space. By contrast to the AdS setting, we show that there are Jordan curves of bounded width which fail to be quasicircles. However, we show that Jordan curves with small width are quasicircles. |
| Databáze: | OpenAIRE |
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