Cyclic quadrilaterals and smooth Jordan curves

2020/11/10 by Joshua Evan Greene, Greene, Joshua Evan, Andrew Lobb +1 · 1 citation
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2011.05216

openalex publication_date 2020/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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