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.References
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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
- MR Author ID: 1084950
- Email: anja289@gmail.com
- Christopher J. Leininger
- Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
- MR Author ID: 688414
- Email: clein@math.uiuc.edu
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 1867-1884
- MSC (2010): Primary 57M50
- DOI: https://doi.org/10.1090/tran/7005
- MathSciNet review: 3739194