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arXiv · 1611.02040

Interrogating surface length spectra and quantifying isospectrality

Hugo Parlier
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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.

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Hugo Parlier. 2016-11-07. Interrogating surface length spectra and quantifying isospectrality. https://arxiv.org/abs/1611.02040

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