Target-local Gromov compactness

Fish, Joel W

doi:10.2140/gt.2011.15.765

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Target-local Gromov compactness

Joel W Fish

Geometry & Topology 15 (2011) 765–826

DOI: 10.2140/gt.2011.15.765

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

Volume 15, issue 2 (2011)