English

On systoles and ortho spectrum rigidity

Geometric Topology 2022-01-19 v3

Abstract

We consider the ortho spectrum of hyperbolic surfaces with totally geodesic boundary. We show that in general the ortho spectrum does not determine the systolic length but that there are only finitely many possibilities. As a corollary we show that, up to isometry, there are only finitely many hyperbolic structures on a surface that share a given ortho spectrum.

Keywords

Cite

@article{arxiv.1909.09829,
  title  = {On systoles and ortho spectrum rigidity},
  author = {Hidetoshi Masai and Greg McShane},
  journal= {arXiv preprint arXiv:1909.09829},
  year   = {2022}
}

Comments

24 pages, 14 figures. with more detailed exposition(v2), added further details(v3)

R2 v1 2026-06-23T11:22:10.968Z