Analytic regularity of CR maps into spheres

الأصل · EN

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