BiLipschitz homogeneous hyperbolic nets

Authors

  • Christopher J. Bishop Stony Brook University, Mathematics Department

Keywords:

BiLipschitz maps, hyperbolic geometry, Margulis constant, homogeneous set, quadrilateral mesh

Abstract

We answer a question of Itai Benjamini by showing there is a K< so that for any ϵ>0, there exist ϵ-dense discrete sets in the hyperbolic disk that are homogeneous with respect to K-biLipschitz maps of the disk to itself. However, this is not true for K close to 1; in that case, every K-biLipschitz homogeneous discrete set must omit a disk of hyperbolic radius ϵ(K)>0. For K=1, this is a consequence of the Margulis lemma for discrete groups of hyperbolic isometries.
Section
Articles

Published

2024-11-26

How to Cite

Bishop, C. J. (2024). BiLipschitz homogeneous hyperbolic nets. Annales Fennici Mathematici, 49(2), 685–694. https://doi.org/10.54330/afm.152404