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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.

Keywords

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

R2 v1 2026-06-22T09:10:25.740Z