Analytic regularity of CR maps into spheres

Abstract

Let M ⊂ CN be a connected real-analytic hypersurface and S2N−1 ⊂ C N′ the unit real sphere, N ′ > N ≥ 2. Assume that M does not contain any complex-analytic hypersurface of CN and that there exists at least one strongly pseudoconvex point on M . We show that any CR map f : M → S2N−1 of class CN−N+1 extends holomorphically to a neighborhood of M in CN .