Quasicircles and width of Jordan curves in $\mathbb{CP}^1$

Autor:	Bonsante, Francesco, Danciger, Jeffrey, Maloni, Sara, Schlenker, Jean-Marc
Rok vydání:	2019
Předmět:	Mathematics - Geometric Topology Mathematics - Differential Geometry 57M50 30C62 30F40 30F60
Druh dokumentu:	Working Paper
DOI:	10.1112/blms.12438
Popis:	We study a notion of "width" for Jordan curves in $\mathbb{CP}^1$, 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. Comment: 18 pages, 11 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1908.09175 Zobrazit plný text záznamu View this record from Arxiv