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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the Schwarz symmetry principle
in a model case


Authors: Joël Merker and Francine Meylan
Journal: Proc. Amer. Math. Soc. 127 (1999), 1097-1102
MSC (1991): Primary 32H02; Secondary 32C05, 32C16
MathSciNet review: 1476379
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Abstract | References | Similar Articles | Additional Information

Abstract: 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.


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Additional Information

Joël Merker
Affiliation: Centre de Mathématiques et d’Informatique, Laboratoire d’Analyse, Topologie et Probabilités, 39 rue Joliot Curie, F-13453 Marseille Cedex 13, France
Email: merker@dmi.ens.fr, merker@gyptis.univ-mrs.fr

Francine Meylan
Affiliation: Université de Fribourg, Institut de Mathématiques, 1700 Perolles, Fribourg, Suisse
Email: meylan@unifr.ch

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04688-2
PII: S 0002-9939(99)04688-2
Keywords: Schwarz symmetry principle, CR mappings, real analytic manifolds
Received by editor(s): July 23, 1997
Additional Notes: The first author was partially supported by the École Normale Supérieure, and the second author by Swiss NSF Grant 2000-042054.94/1.
Communicated by: Steven R. Bell
Article copyright: © Copyright 1999 American Mathematical Society