Journal of Symplectic Geometry

Compactness for punctured holomorphic curves

K. Cieliebak and K. Mohnke

Full-text: Open access

Abstract

Bourgeois, Eliashberg, Hofer, Wysocki and Zehnder recently proved a general compactness result for moduli spaces of punctured holomorphic curves arising in symplectic field theory. In this paper we present an alternative proof of this result. The main idea is to determine a priori the levels at which holomorphic curves split, thus reducing the proof to two separate cases: long cylinders of small area, and regions with compact image. The second case requires a generalization of Gromov compactness for holomorphic curves with free boundary.

Article information

Source
J. Symplectic Geom., Volume 3, Number 4 (2005), 589-654.

Dates
First available in Project Euclid: 1 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1154467631

Mathematical Reviews number (MathSciNet)
MR2235856

Zentralblatt MATH identifier
1113.53053

Citation

Cieliebak , K.; Mohnke, K. Compactness for punctured holomorphic curves. J. Symplectic Geom. 3 (2005), no. 4, 589--654. https://projecteuclid.org/euclid.jsg/1154467631


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