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Transactions of the American Mathematical Society

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Marked-length-spectral rigidity for flat metrics


Authors: Anja Bankovic and Christopher J. Leininger
Journal: Trans. Amer. Math. Soc. 370 (2018), 1867-1884
MSC (2010): Primary 57M50
DOI: https://doi.org/10.1090/tran/7005
Published electronically: October 31, 2017
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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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Additional Information

Anja Bankovic
Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02459
Address at time of publication: Cara Lazara 2/6, 34220 Laovo, Serbia
Email: anja289@gmail.com

Christopher J. Leininger
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Email: clein@math.uiuc.edu

DOI: https://doi.org/10.1090/tran/7005
Received by editor(s): July 16, 2015
Received by editor(s) in revised form: June 16, 2016
Published electronically: October 31, 2017
Additional Notes: The second author was partially supported by NSF grants DMS-1207183 and DMS-1510034
Article copyright: © Copyright 2017 American Mathematical Society

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