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arXiv · 2412.01777

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

Alberto Abbondandolo·Oliver Edtmair·Jungsoo Kang
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Abstract

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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Alberto Abbondandolo, Oliver Edtmair, Jungsoo Kang. 2024-12-02. On closed characteristics of minimal action on a convex three-sphere. https://arxiv.org/abs/2412.01777

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