Periodicity characterization by capacities for star-shaped domains
Abstract
We complete the spectral characterization of Besse and Zoll Reeb flows on the standard contact sphere S2n-1 initiated by Ginzburg-G\"urel-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.
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