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arXiv · 1508.07542

Dense existence of periodic Reeb orbits and ECH spectral invariants

Kei Irie
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Abstract

In this paper, we prove (1): for any closed contact three-manifold with a $C^\infty$-generic contact form, the union of periodic Reeb orbits is dense, (2): for any closed surface with a $C^\infty$-generic Riemannian metric, the union of closed geodesics is dense. The key observation is $C^\infty$-closing lemma for 3D Reeb flows, which follows from the fact that the embedded contact homology (ECH) spectral invariants recover the volume.

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Kei Irie. 2015-10-22. Dense existence of periodic Reeb orbits and ECH spectral invariants. https://arxiv.org/abs/1508.07542

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