English

Interrogating surface length spectra and quantifying isospectrality

Differential Geometry 2016-11-08 v1 Geometric Topology Spectral Theory

Abstract

This article is about inverse spectral problems for hyperbolic surfaces and in particular how length spectra relate to the geometry of the underlying surface. A quantitative answer is given to the following: how many questions do you need to ask a length spectrum to determine it completely? In answering this, a quantitative upper bound is given on the number of isospectral but non-isometric surfaces of a given genus.

Keywords

Cite

@article{arxiv.1611.02040,
  title  = {Interrogating surface length spectra and quantifying isospectrality},
  author = {Hugo Parlier},
  journal= {arXiv preprint arXiv:1611.02040},
  year   = {2016}
}

Comments

32 pages, 10 figures

R2 v1 2026-06-22T16:44:09.510Z