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

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.

### MSC:

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