Whitney's embedding theorem for pseudo-holomorphic discs
The main result of this paper consist in proving the followingNEWLINENEWLINE{ Theorem 1.1.} Let \((M,J)\) be a \(C^{\infty}\)-smooth almost complex manifold of complex dimension \(\geq 3\). Fix \(m\geq 0\) and let \(f_0:{\overline{\mathbb D}}\to M\) be a \(J\)-holomorphic map of class \(C^m{(\overline{\mathbb D})}\). Then there exists a \(J\)-holomorphic imbedding \(f:{\overline{\mathbb D}}\to M\) arbitrarily close to \(f_0\) in \(C^m{(\overline{\mathbb D})}\).NEWLINENEWLINEHere \(\mathbb D\) stands for the unit disc in \({\mathbb C}\).
scientific article; zbMATH DE number 6215479