On the proof of Kuranishi's embedding theorem (Q1822662)

The author proves a local holomorphic embedding theorem for a formally integrable, strictly pseudoconvex CR manifold M with dim M\(=2n-1\geq 7\). The proof is based on Nash-Moser methods and estimates for the Khenkin operators obtained recently by the author (see the previous review). If M is of class \(C^ m\), an embedding of class \(C^ k\) is obtained, with m and k suitably related, whereas previous results were for M of class \(C^{\infty}\). More importantly, the author's argument is significantly simpler than previous ones. In view of Rossi's example of a 3-dimensional M which cannot be embedded into \({\mathbb{C}}^ N\), only the case dim M\(=5\) remains open.