#### Volume 15, issue 2 (2011)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
Target-local Gromov compactness

### Joel W Fish

Geometry & Topology 15 (2011) 765–826
##### Abstract

We prove a version of Gromov’s compactness theorem for pseudoholomorphic curves which holds locally in the target symplectic manifold. This result applies to sequences of curves with an unbounded number of free boundary components, and in families of degenerating target manifolds which have unbounded geometry (eg no uniform energy threshold). Core elements of the proof regard curves as submanifolds (rather than maps) and then adapt methods from the theory of minimal surfaces.

##### Keywords
pseudoholomorphic, compactness, pseudoholomorphic, target-local, $J$–curve
Primary: 32Q65
Secondary: 53D99