English

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.

Keywords

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}
}
R2 v1 2026-06-24T03:35:04.945Z