A Theorem of Wolpert, and some Variations

Ludovico Battista; Nolwenn Le Quellec; Juan Souto

A Theorem of Wolpert, and some Variations

Geometric Topology 2026-07-14 v1

Authors: Ludovico Battista , Nolwenn Le Quellec , Juan Souto

Abstract

We give a streamlined proof of the fact that generically, isospectral hyperbolic surfaces are isometric. We also prove some versions of this result allowing for quasi-Fuchsian groups or considering the simple length spectrum.

Keywords

isospectral hyperbolic surfaces isometric quasi-Fuchsian groups simple length spectrum

Cite

@article{arxiv.2607.12977,
  title  = {A Theorem of Wolpert, and some Variations},
  author = {Ludovico Battista and Nolwenn Le Quellec and Juan Souto},
  journal= {arXiv preprint arXiv:2607.12977},
  year   = {2026}
}

Comments

15 pages + biblio. Comments are welcome!