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On closed characteristics of minimal action on a convex three-sphere
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On closed characteristics of minimal action on a convex three-sphere
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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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Cited by 1 Pith paper
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The strong Arnol'd chord conjecture for the boundary of a uniformly convex domain in $\mathbb{R}^{4}$
Proves that any E3 Legendrian in the boundary of a Liouville domain bounds a chord of length at most liminf c_k(Ω)/k and applies this to establish the strong Arnol'd chord conjecture for uniformly convex domains in R^4.
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