Remarks about the \(C^{\infty }\)-closing lemma for 3-dimensional Reeb flows

DOI10.1215/21562261-2021-0003zbMath1485.53098OpenAlexW3156845768WikidataQ125064111 ScholiaQ125064111MaRDI QIDQ2038537

Kei Irie

Publication date: 7 July 2021

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/21562261-2021-0003

zbMATH Keywords

embedded contact homologyclosing lemmaperiodic Reeb orbits

Mathematics Subject Classification ID

Contact manifolds (general theory) (53D10) Symplectic field theory; contact homology (53D42)

Cites Work

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• Beyond ECH capacities
• Proof of the Arnold chord conjecture in three dimensions. II
• Embedded contact homology and Seiberg-Witten Floer cohomology. V.
• Quantitative embedded contact homology
• Dense existence of periodic Reeb orbits and ECH spectral invariants
• A proof of Weinstein's conjecture in \(\mathbb R^{2n}\)
• Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three
• Sub-leading asymptotics of ECH capacities
• An estimate on energy of min-max Seiberg-Witten Floer generators
• Torsion contact forms in three dimensions have two or infinitely many Reeb orbits
• Symplectic embeddings from concave toric domains into convex ones
• Equidistribution of minimal hypersurfaces for generic metrics
• The Seiberg-Witten equations and the Weinstein conjecture
• The asymptotics of ECH capacities
• Symplectic embeddings into four-dimensional concave toric domains
• Lecture Notes on Embedded Contact Homology
• The C¹ Closing Lemma, including Hamiltonians
• The Closing Lemma
• From one Reeb orbit to two

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