On the strong Arnold chord conjecture for convex contact forms

2023/04/14 by Jungsoo Kang, Kang, Jungsoo · 1 citation
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2304.07016

openalex publication_date 2023/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The original Arnold chord conjecture states that every closed Legendrian submanifold of the standard contact sphere S^2n-1 admits a Reeb chord with distinct endpoints with respect to any contact form. In this paper, we prove this conjecture for contact forms induced by strictly convex embeddings into ℝ²ⁿ under the assumption that minimal periodic Reeb orbits are of Morse-Bott type. We also provide a counterexample when the convexity condition is not satisfied.

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