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arXiv · 2304.07016

On the strong Arnold chord conjecture for convex contact forms

Jungsoo Kang
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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 $\mathbb{R}^{2n}$ 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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Jungsoo Kang. 2023-04-14. On the strong Arnold chord conjecture for convex contact forms. https://arxiv.org/abs/2304.07016

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