Marked-length-spectral rigidity for flat metrics

Anja Bankovic, Christopher J. Leininger

Research output: Contribution to journalArticlepeer-review


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 conjecture for this class of metrics.

Original languageEnglish (US)
Pages (from-to)1867-1884
Number of pages18
JournalTransactions of the American Mathematical Society
Issue number3
StatePublished - 2018

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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