2009/12/31 by Joel W. Fish · 1 citation
Mathematics · #math.SG #math.AP #math.DG #msc:32Q65 #msc:53D99
paper · pdf · doi:10.2140/gt.2011.15.765
published as Geom. Topol. 15 (2011) 765-826 · 49 Pages. Modifications: NSF grant support updated.
arxiv created 2010/05/05 · arxiv updated 2014/11/11
We prove a version of Gromov's compactness theorem for pseudo-holomorphic 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 (e.g. 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.