2026/02/23 by Federica Fanoni, David Fisac
#math.GT #math.DG
We study infinite-type hyperbolic surfaces with discrete length spectrum. In this setup, we show that Sunada's method can only produce finite isospectral families, but that there is no bound on the cardinality of an isospectral family (for any infinite-type surface without planar ends). We then prove that, given any infinite-genus surface satisfying an additional topological assumption, any finite group can be realized as isometry group of a hyperbolic structure with discrete length spectrum.