Target-local Gromov compactness

• Main Author: Fish, Joel W
• Format: Journal Article
• Language: English
• Published: 05-05-2010
• Subjects: Mathematics - Analysis of PDEs; Mathematics - Differential Geometry; Mathematics - Symplectic Geometry
• DOI: 10.48550/arxiv.0912.4435

Geom. Topol. 15 (2011) 765-826 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.