On the structure of Besse convex contact spheres

Mazzucchelli, Marco; Radeschi, Marco

doi:10.1090/tran/8836

On the structure of Besse convex contact spheres
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by Marco Mazzucchelli and Marco Radeschi;

Trans. Amer. Math. Soc. 376 (2023), 2125-2153

DOI: https://doi.org/10.1090/tran/8836

Published electronically: December 15, 2022

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Abstract:

We consider convex contact spheres $Y$ all of whose Reeb orbits are closed. Any such $Y$ admits a stratification by the periods of closed Reeb orbits. We show that $Y$ “resembles” a contact ellipsoid: any stratum of $Y$ is an integral homology sphere, and the sequence of Ekeland-Hofer spectral invariants of $Y$ coincides with the full sequence of action values, each one repeated according to its multiplicity.

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