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

The annulus property of simple holomorphic discs