A Finsler counterexample to the Croke conjecture for the systolic ratio\n on the 2-sphere

2021/06/03 by Guillaume Buro, Buro, Guillaume, Louis Merlin +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Mathematics and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2106.01849

openalex publication_date 2021/06/03 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We exhibit a Finsler metric on the 2-sphere whose systolic (Holmes-Thompson)\nratio is frac4\π3. This is bigger than the conjectured maximal\nRiemannian systolic ratio of 2\√(3) achieved by the Calabi-Croke metric.\nThe construction of the Finsler metric is heavily inspired by a paper of\nCossarini-Sabourau.\n

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