%0 Journal Article
%T Length spectra and degeneration of flat metrics
%A Moon Duchin
%A Christopher J. Leininger
%A Kasra Rafi
%J Mathematics
%D 2009
%I arXiv
%R 10.1007/s00222-010-0262-y
%X In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the length vector determines a metric among the class of flat metrics. Secondly, we give an embedding into the space of geodesic currents and use this to get a boundary for the space of flat metrics. The geometric interpretation is that flat metrics degenerate to "mixed structures" on the surface: part flat metric and part measured foliation.
%U http://arxiv.org/abs/0907.2082v1