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The annulus property of simple holomorphic discs. (English) Zbl 1273.32030

Summary: 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.

MSC:

32Q60 Almost complex manifolds
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