Marked length spectral rigidity for flat metrics
Geometric Topology
2015-04-07 v1 Differential Geometry
Group Theory
Abstract
In this paper we prove that the space of flat metrics (nonpositively curved Euclidean cone metrics) on a closed, oriented surface is marked length spectrally rigid. In other words, two flat metrics assigning the same lengths to all closed curves differ by an isometry isotopic to the identity. The novel proof suggests a stronger rigidity result for flat metrics.
Cite
@article{arxiv.1504.01159,
title = {Marked length spectral rigidity for flat metrics},
author = {Anja Bankovic and Christopher J. Leininger},
journal= {arXiv preprint arXiv:1504.01159},
year = {2015}
}
Comments
18 pages, 6 figures