Minimizing laminations in regular covers, horospherical orbit closures, and circle-valued Lipschitz maps

Autor:	Farre, James, Landesberg, Or, Minsky, Yair
Rok vydání:	2023
Předmět:	Mathematics - Dynamical Systems Mathematics - Geometric Topology 37D40 57K20 (Primary) 37A17 30F60 22F30 57K32 37B20 37B99 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We expose a connection between distance minimizing laminations and horospherical orbit closures in $\mathbb{Z}$-covers of compact hyperbolic manifolds. For surfaces, we provide novel constructions of $\mathbb{Z}$-covers with prescribed geometric and dynamical properties, in which an explicit description of all horocycle orbit closures is given. We further show that even the slightest of perturbations to the hyperbolic metric on a $\mathbb{Z}$-cover can lead to drastic topological changes to horocycle orbit closures. Comment: 62 pages, 16 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.14296 Zobrazit plný text záznamu View this record from Arxiv