The strong Arnol'd chord conjecture for the boundary of a uniformly convex domain in ℝ⁴

2026/06/22 by Dylan Cant · 1 voice
Mathematics · #math.SG

paper · pdf

Abstract

Following the idea of Jungsoo Kang and Jun Zhang, we prove the strong Arnol'd chord conjecture for the boundary of a uniformly convex domain in ℝ⁴, using an ellipsoid embedding construction due to Oliver Edtmair. We prove a general structural result for Legendrians L which are eventually equivariantly essential (E3), in the sense that the kth Gutt-Hutchings capacity c_k(D^*TL) is infinite for k large enough. We show that any E3 Legendrian in the boundary of a Liouville domain Ω bounds a chord of length at most \liminf c_k(Ω)/k.

Citations

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Discussions

• Dylan Cant: The strong Arnol'd chord conjecture for the boundary of a uniformly convex domain in $\mathbb{R}^{4}$ https://arxiv.org/abs/2606.23663 https://arxiv.org/pdf/2606.23663 https://arxiv.org/ht [bsky, 0 points, 0 comments]

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• Strong Arnold chord conjecture via normalized capacities
• Lengths of Reeb chords and Viterbo restriction
• Lagrangian capacity and chain level string topology
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