Singularities of \(J\)-holomorphic curves (Q1380096)

We prove a result of M. Micallef and B. White: a germ of \(J\)-holomorphic curve in an almost complex manifold is \(C^1\)-equivalent to a germ of complex curve in \(\mathbb{C}^n\). We give an example showing that this cannot be improved to \(C^2\) even if \(J\) is real analytic. Finally we deduce a global version: for every \(J\)-curve there is a complex structure on some neighbourhood with respect to which the curve is still complex.