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arxiv: 2412.01777 · v1 · pith:QQL2FGOL · submitted 2024-12-02 · math.SG · math.DS

On closed characteristics of minimal action on a convex three-sphere

Alberto Abbondandolo , Oliver Edtmair , Jungsoo Kang This is my paper

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classification math.SG math.DS
keywords actionclosedconvexminimalboundarycharacteristicbodybounds
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We prove that every closed characteristic of minimal action on the boundary of a uniformly convex domain in $\R^4$ bounds a disk-like global surface of section. A corollary is that the cylindrical symplectic capacity of a convex body in $\R^4$ coincides with the minimal action of a closed generalized characteristic on its boundary.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The strong Arnol'd chord conjecture for the boundary of a uniformly convex domain in $\mathbb{R}^{4}$

    math.SG 2026-06 unverdicted novelty 6.0

    Proves that any E3 Legendrian in the boundary of a Liouville domain bounds a chord of length at most liminf c_k(Ω)/k and applies this to establish the strong Arnol'd chord conjecture for uniformly convex domains in R^4.