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arXiv · 2511.18401

Periodicity characterization by capacities for star-shaped domains

Jean Gutt·Vinicius G. B. Ramos·Shira Tanny
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Abstract

We complete the spectral characterization of Besse and Zoll Reeb flows on the standard contact sphere $S^{2n-1}$ initiated by Ginzburg-G\"urel-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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Jean Gutt, Vinicius G. B. Ramos, Shira Tanny. 2025-11-23. Periodicity characterization by capacities for star-shaped domains. https://arxiv.org/abs/2511.18401

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