Extremal discs and the regularity of CR mappings in higher codimension (Q2731390)

The author develops a local theory of extremal analytic discs for a strictly pseudoconvex manifold of higher codimension in complex space. Then the author applies the results to the question of the regularity of CR mappings.NEWLINENEWLINENEWLINEUnder a suitable condition on the CR manifolds \(M, N\), the author proves that a CR homeomorphism \(F\) from \(M\) to \(N\) such that both \(F\) and its inverse satisfy a Lipschitz condition with some exponent between \(0\) and \(1\) is actually \(C^\infty\) smooth. In the hypersurface case, this reduces to Fefferman's theorem.NEWLINENEWLINENEWLINEThe idea of the proof is to observe that a CR mapping preserves the so called lifts of the extremal discs and use a smooth version of the Schwarz reflection principle.