Periodicity characterization by capacities for star-shaped domains

2025/11/23 by Gutt, Jean, Ramos, Vinicius G. B., Tanny, Shira · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Geometry and complex manifolds

paper · doi:10.48550/arxiv.2511.18401

Abstract

We complete the spectral characterization of Besse and Zoll Reeb flows on the standard contact sphere S^2n-1 initiated by Ginzburg-Gürel-Mazzucchelli. Roughly speaking, it states that a Reeb flow on the boundary of any star-shaped domain in ℝ²ⁿ is Besse if and only if it has n coinciding Ekeland-Hofer capacities, and that it is Zoll if and only if the first n capacities coincide.

Citations

• On Zoll Contact 5-Spheres
• The equivalence of Ekeland-Hofer and equivariant symplectic homology capacities
• Positive (S¹-equivariant) symplectic homology of convex domains, higher capacities, and Clarke's duality
• Closed Orbits of Dynamically Convex Reeb Flows: Towards the HZ- and Multiplicity Conjectures
• Contact homology and higher dimensional closing lemmas
• The equivariant pair-of-pants product in fixed point Floer cohomology
• Generalized Conley-Zehnder index
• Symplectic homology, autonomous Hamiltonians, and Morse-Bott moduli spaces

Cited by

• A note on the wild symplectic ellipsoids
• Hamiltonian linking and Symplectic packing

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• Dynamically exotic contact spheres in dimensions ≥ 7