The annulus property of simple holomorphic discs

Details The annulus property of simple holomorphic discs The annulus property of simple holomorphic discs

2010-03-09

arxiv.org/abs/1003.1842v3

Mathematics

Symplectic Geometry

23 pages, no figures, article rewritten, to appear in J. Symplectic Geom

Scientific paper

We show that any simple holomorphic disc admits the annulus property, i.e., each interior point is surrounded by an arbitrary small annulus consisting entirely of injective points. As an application we show that interior singularities of holomorphic discs can be resolved after slight perturbation of the almost complex structure. Moreover, for boundary points the analogue notion, the half-annulus property, is introduced and studied in detail.

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