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Cyclic quadrilaterals and smooth Jordan curves

Greene, Joshua Evan; Lobb, Andrew

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Authors

Joshua Evan Greene



Contributors

Abstract

For every smooth Jordan curve γ and cyclic quadrilateral Q in the Euclidean plane, we show that there exists an orientation-preserving similarity taking the vertices of Q to γ. The proof relies on the theorem of Polterovich and Viterbo that an embedded Lagrangian torus in C2 has minimum Maslov number 2.

Citation

Greene, J. E., & Lobb, A. (2023). Cyclic quadrilaterals and smooth Jordan curves. Inventiones Mathematicae, 234(3), 931–935. https://doi.org/10.1007/s00222-023-01212-6

Journal Article Type Article
Acceptance Date Jul 25, 2023
Online Publication Date Aug 2, 2023
Publication Date 2023
Deposit Date Aug 24, 2023
Publicly Available Date Aug 3, 2024
Journal Inventiones mathematicae
Print ISSN 0020-9910
Electronic ISSN 1432-1297
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 234
Issue 3
Pages 931–935
DOI https://doi.org/10.1007/s00222-023-01212-6
Public URL https://durham-repository.worktribe.com/output/1724240

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Accepted Journal Article (322 Kb)
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Copyright Statement
This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00222-023-01212-6





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