Bounded geometry with no bounded pants decomposition
Geometric Topology
2021-06-28 v1 Complex Variables
Abstract
We construct a quasiconformally homogeneous hyperbolic Riemann surface-other than the hyperbolic plane-that does not admit a bounded pants decomposition. Also, given a connected orientable topological surface of infinite type with compact boundary components, we construct a complete hyperbolic metric on the surface that has bounded geometry but does not admit a bounded pants decomposition.
Cite
@article{arxiv.2106.13406,
title = {Bounded geometry with no bounded pants decomposition},
author = {Ara Basmajian and Hugo Parlier and Nicholas G. Vlamis},
journal= {arXiv preprint arXiv:2106.13406},
year = {2021}
}