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arXiv · 1310.8276

A Bound on Length Isospectral Families of Hyperbolic Surfaces

Weston Ungemach
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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.

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Weston Ungemach. 2014-03-24. A Bound on Length Isospectral Families of Hyperbolic Surfaces. https://arxiv.org/abs/1310.8276

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