Journal of Symplectic Geometry

Volume 11 (2013)

Number 1

The annulus property of simple holomorphic discs

Pages: 135 – 161



Kai Zehmisch (Mathematisches Institut, Universität zu Köln, Germany)


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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