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arXiv · 2606.20468

Rigidity of coarsely minimal Reeb flows

Barney Bramham·Jacobus S. de Pooter
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Abstract

We introduce the notion of a coarsely minimal Reeb flow, generalizing the notion of minimal geodesic flow, and prove the following rigidity theorem: That a coarsely minimal Reeb flow satisfying a divergence property is orbitally equivalent to the geodesic flow of a Riemannian metric of negative sectional curvature. Without the divergence assumption, we obtain an orbital semi-equivalence. This extends a rigidity result for geodesic flows of negatively curved Riemannian metrics which is due to Gromov. We use Floer homology and Morse's hyperbolic `stability' Lemma.

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Barney Bramham, Jacobus S. de Pooter. 2026-06-18. Rigidity of coarsely minimal Reeb flows. https://arxiv.org/abs/2606.20468

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