%0 Journal Article %T On the Schwarz Symmetry Principle in a Model Case %+ Laboratoire de Mathématiques d'Orsay (LMO) %+ Université de Fribourg = University of Fribourg (UNIFR) %A Merker, Joël %A Meylan, Francine %< avec comité de lecture %@ 0002-9939 %J Proceedings of the American Mathematical Society %I American Mathematical Society %V 127 %N 4 %P 1097-1102 %8 1999 %D 1999 %K Schwarz symmetry principle %K CR mappings %K real analytic manifolds %K Schwarz symmetry principle %Z 1991 MSC: Primary 32H02; Secondary 32C05, 32C16. %Z Mathematics [math]Journal articles %X 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. %G English %2 https://universite-paris-saclay.hal.science/hal-03285202/document %2 https://universite-paris-saclay.hal.science/hal-03285202/file/merker-meylan-1997.pdf %L hal-03285202 %U https://universite-paris-saclay.hal.science/hal-03285202 %~ CNRS %~ UNIV-PSUD %~ INSMI %~ LM-ORSAY %~ UNIV-PARIS-SACLAY %~ UNIV-PSUD-SACLAY %~ GS-MATHEMATIQUES