Dense existence of periodic Reeb orbits and ECH spectral invariants
By Kei Irie. 2015
62 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4942770c65f62286a6f01b07a3758d82386a8217
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Citations in the corpus
- Density of minimal hypersurfaces for generic metrics. (2017, methodology): “The argument of [8] is based on a different kind of asymptotic law, involving spectral invariants in Embedded Contact Homology ([4]).”
- Torsion contact forms in three dimensions have two or infinitely many Reeb orbits (2017, unknown): “We remark that the volume property was also used in [4] to prove Theorem 1.1 above; for some additional applications of the volume property, see Asaoka and Irie [1], Hutchings [16] and Irie [22].”