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Finite energy cylinders of small area

Published online by Cambridge University Press:  02 October 2002

H. HOFER,
K. WYSOCKI and
E. ZEHNDER
H. HOFER
Affiliation:
Courant Institute, 251 Mercer Street, New York, NY 10012, USA (e-mail: hofer@cims.nyu.edu)
K. WYSOCKI
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia
E. ZEHNDER
Affiliation:
Department of Mathematics, ETH Zürich, CH-8092 Zürich, Switzerland
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Abstract

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\widetilde{J}-holomorphic cylinders in \mathbb{R}\times M, where M is a contact manifold are investigated. It is shown that a sufficiently long cylinder having small area is close to a constant map, if its center action vanishes. If its center action is positive, it is close to a cylinder over a periodic orbit of the Reeb vector field, and has a well-determined shape. A compactness result is deduced, which is useful in symplectic field theory.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 5 , October 2002, pp. 1451 - 1486
Copyright
© 2002 Cambridge University Press