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Periodicity characterization by capacities for star-shaped domains (2511.18401v1)
Published 23 Nov 2025 in math.SG
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 $\mathbb{R}{2n}$ 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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