Length spectra and degeneration of flat metrics
By Moon Duchin, Christopher J. Leininger, Kasra Rafi. 2009
110 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fcf4aa6589eaaca3ede4f70e9ca457629a55ae52
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Counting curves in hyperbolic surfaces (2015, background): “More precisely, fixing for the sake of concreteness a distance d : CK(Σ) × CK(Σ) → R+ inducing the topology of CK(Σ) (see [6] for a concrete choice), we prove:”