Journal of Differential Geometry

From one Reeb orbit to two

Daniel Cristofaro-Gardiner and Michael Hutchings

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Abstract

We show that every (possibly degenerate) contact form on a closed three-manifold has at least two embedded Reeb orbits. We also show that if there are only finitely many embedded Reeb orbits, then their symplectic actions are not all integer multiples of a single real number; and if there are exactly two embedded Reeb orbits, then the product of their symplectic actions is less than or equal to the contact volume of the manifold. The proofs use a relation between the contact volume and the asymptotics of the amount of symplectic action needed to represent certain classes in embedded contact homology, recently proved by the authors and V. Ramos.

Article information

Source
J. Differential Geom., Volume 102, Number 1 (2016), 25-36.

Dates
First available in Project Euclid: 5 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1452002876

Digital Object Identifier
doi:10.4310/jdg/1452002876

Mathematical Reviews number (MathSciNet)
MR3447085

Zentralblatt MATH identifier
1338.53108

Citation

Cristofaro-Gardiner, Daniel; Hutchings, Michael. From one Reeb orbit to two. J. Differential Geom. 102 (2016), no. 1, 25--36. doi:10.4310/jdg/1452002876. https://projecteuclid.org/euclid.jdg/1452002876


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