A Bound on Length Isospectral Families of Hyperbolic Surfaces
Metric Geometry
2014-03-25 v3 Geometric Topology
Abstract
In this paper we obtain a bound on the number of isometry classes of finite area hyperbolic surfaces which are length isospectral to a given surface depending only on the topological type of the surface and the length of the shortest closed geodesic on the surface. This will follow from a more general bound applying to any family of hyperbolic surfaces which admits a Bers' constant and with a lower bound on systole length.
Keywords
Cite
@article{arxiv.1310.8276,
title = {A Bound on Length Isospectral Families of Hyperbolic Surfaces},
author = {Weston Ungemach},
journal= {arXiv preprint arXiv:1310.8276},
year = {2014}
}