On the Schwarz Symmetry Principle in a Model Case

Joël Merker (1) , Francine Meylan (2)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 UNIFR - Université de Fribourg = University of Fribourg

In this article, we prove that smooth CR diffeomorphisms between two real analytic holomorphically nondegenerate hypersurfaces, one of which is rigid and polynomial, extend to be locally biholomorphic. It turns out that the result can be generalized to not totally degenerate mappings, in the sense of Baouendi and Rothschild.

Keywords: Schwarz symmetry principle; CR mappings; real analytic manifolds; Schwarz symmetry principle

Domains: Mathematics [math]

Joël Merker, Francine Meylan. On the Schwarz Symmetry Principle in a Model Case. Proceedings of the American Mathematical Society, 1999, 127 (4), pp.1097-1102. ⟨hal-03285202⟩