Analyticity of smooth CR mappings of generic submanifolds (Q2472605)

Let \(f\) be be a smooth CR mapping from a real analytic submanifold \(M\) in \(\mathbb{C}^N\) into \(\mathbb{C}^N\). Suppose that \(M\) is of finite type and essentially finite at a point \(p\in M\) and that \(f\) is formally finite at \(p\). In this paper, the authors give a necessary and sufficient condition that \(f\) extends as a holomorphic mapping in some neighborhood of \(p\). The condition is the existence of an irreducible real analytic subvariety \(\widetilde X\) in \(\mathbb{C}^N\) such that \(f(M)\subset \widetilde X\).