Length spectra and degeneration of flat metrics

Details Length spectra and degeneration of flat metrics Length spectra and degeneration of flat metrics

2009-07-13

arxiv.org/abs/0907.2082v1

Mathematics

Geometric Topology

36 pages

Scientific paper

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.

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