Erlandsson, VivekaLeininger, Christopher J.Sadanand, Chandrika2022-09-292022-09-292022Erlandsson, Viveka, Leininger, Christopher J. and Sadanand, Chandrika. "Hyperbolic cone metrics and billiards." <i>Advances in Mathematics,</i> 409, no. Part B (2022) Elsevier: https://doi.org/10.1016/j.aim.2022.108662.https://hdl.handle.net/1911/113418A negatively curved hyperbolic cone metric is called rigid if it is determined (up to isotopy) by the support of its Liouville current, and flexible otherwise. We provide a complete characterization of rigidity and flexibility, prove that rigidity is a generic property, and parameterize the associated deformation space for any flexible metric. As an application, we parameterize the space of hyperbolic polygons with the same symbolic coding for their billiard dynamics, and prove that generically this parameter space is a point.engThis is an open access article under the CC BY licenseJournal article1-s2-0-S0001870822004790-mainhttps://doi.org/10.1016/j.aim.2022.108662