Marked-length-spectral rigidity for flat metrics

Bankovic, Anja; Leininger, Christopher

doi:10.1090/tran/7005

Marked-length-spectral rigidity for flat metrics
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by Anja Bankovic and Christopher J. Leininger PDF

Trans. Amer. Math. Soc. 370 (2018), 1867-1884 Request permission

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 conjecture for this class of metrics.

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