TY - JOUR
T1 - Length spectra and degeneration of flat metrics
AU - Duchin, Moon
AU - Leininger, Christopher J.
AU - Rafi, Kasra
N1 - Funding Information:
The first author is partially supported by NSF grant DMS-0906086. The second author is partially supported by NSF grant DMS-0905748.
PY - 2010
Y1 - 2010
N2 - 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 obtain a compactification 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.
AB - 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 obtain a compactification 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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U2 - 10.1007/s00222-010-0262-y
DO - 10.1007/s00222-010-0262-y
M3 - Article
AN - SCOPUS:77957947582
SN - 0020-9910
VL - 182
SP - 231
EP - 277
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 2
ER -