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arXiv · 2404.05150

Strong Arnold chord conjecture via normalized capacities

Jungsoo Kang·Jun Zhang
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Abstract

We show that every dynamically convex toric domain in $\mathbb R^4$ admits a $C^1$-neighborhood $\mathcal U$ within the space of star-shaped domains of $\mathbb R^4$ with the following property: for any $X \in \mathcal U$, every Legendrian knot in $\partial X$ admits a Reeb chord with distinct endpoints. A higher dimensional analog is also discussed.

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Jungsoo Kang, Jun Zhang. 2024-04-08. Strong Arnold chord conjecture via normalized capacities. https://arxiv.org/abs/2404.05150

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