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Strong Arnold chord conjecture via normalized capacities
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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.
Forward citations
Cited by 2 Pith papers
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Lengths of Reeb chords and Viterbo restriction
Products of spheres yield n-invertible cotangent bundles, so every compact Legendrian in ST*M has a Reeb chord of length at most the n-invertibility capacity.
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Hamiltonian linking and Symplectic packing
Hamiltonian unlinked subsets of a symplectic ball satisfy the spectral capacity packing inequality c(K1) + c(K2) <= a, and violating that inequality forces Hamiltonian linking.
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