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