Length spectra and degeneration of flat metrics
Geometric Topology
2015-05-13 v1 Metric Geometry
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.
Keywords
Cite
@article{arxiv.0907.2082,
title = {Length spectra and degeneration of flat metrics},
author = {Moon Duchin and Christopher J. Leininger and Kasra Rafi},
journal= {arXiv preprint arXiv:0907.2082},
year = {2015}
}
Comments
36 pages