On the Schwarz symmetry principle in a model case. (English) Zbl 0919.32011

Merker, Joël; Meylan, Francine

Proc. Am. Math. Soc. 127, No. 4, 1097-1102 (1999).

Let \(f:M\rightarrow M'\) be a \(C^{\infty}\)-smooth CR diffeomorphism between real analytic, holomorphically non degenerate hypersurfaces in \(\mathbb{C^n}\), which is holomorphic on one side of \(M\). The authors establish the Schwarz symmetry principle in case \(M'\) is in addition rigid and polynomial. It is not required that \(M\) be algebraic.

Reviewer: Martin Chuaqui (Santiago de Chile)

MSC:

32H02	Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables
32C05	Real-analytic manifolds, real-analytic spaces
32V99	CR manifolds

Keywords:

Schwarz symmetry principle; CR mappings; real analytic manifolds