Volume 15, issue 2 (2011)

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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
Mathematical Subject Classification 2000
Primary: 32Q65
Secondary: 53D99
References
Publication
Received: 26 August 2010
Accepted: 31 January 2011
Published: 23 May 2011
Proposed: Yasha Eliashberg
Seconded: Leonid Polterovich, Simon Donaldson
Authors
Joel W Fish
Department of Mathematics
Stanford University
Stanford CA 94305
USA
http://www.stanford.edu/~joelfish