Length spectra and degeneration of flat metrics

Moon Duchin; Christopher J. Leininger; Kasra Rafi

doi:10.1007/s00222-010-0262-y

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arXiv · 0907.2082

Length spectra and degeneration of flat metrics

Moon Duchin·Christopher J. Leininger·Kasra Rafi

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Abstract

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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BibTeX RIS

Moon Duchin, Christopher J. Leininger, Kasra Rafi. 2009-07-13. Length spectra and degeneration of flat metrics. https://doi.org/10.1007/s00222-010-0262-y

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