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On the Schwarz symmetry principle in a model case
Author(s):
Joël
Merker;
Francine
Meylan
Journal:
Proc. Amer. Math. Soc.
127
(1999),
1097-1102.
MSC (1991):
Primary 32H02;
Secondary 32C05, 32C16
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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.
References:
- [BJT]
- S. Baouendi, H. Jacobowitz and F. Treves, On the real analyticity of CR mappings, Ann. Math. 122 (1985), 365-400. MR 87f:32044
- [BR]
- S. Baouendi and L. Rothschild,, Germs of CR maps between hypersurfaces in complex space, Invent. Math. 93 (1988), 481-500. MR 90a:32036
- [BHR]
- S. Baouendi, X. Huang and L. Rothschild, Regularity of CR mappings between algebraic hypersurfaces, Invent. Math. 125 (1996), 13-36.
- [MER]
- J. Merker, On the Schwarz symmetry principle in three-dimensional complex euclidean space, Publications du Laboratoire de Mathématiques de l'École Normale Supérieure, Paris, Juillet 1997. Available at: http://www.dmi.ems.fr/edition/preprints
- [MEY]
- F. Meylan, A reflection principle un complex space for a class of hypersurfaces and mappings, Pacific Math. J. 169 (1995), 135-160. MR 96f:32018
- [MM]
- F. Meylan and H.-M. Maire, Extension of smooth CR mappings between non essentially finite hypersurfaces in
 , Ark. Mat. 35 (1997), 185-199. CMP 97:11 - [MIR]
- N. Mir, An algebraic characterization of holomorphic degeneracy and analyticity of CR mappings, Preprint, 1997.
- [S]
- N. Stanton, Infinitesimal CR automorphisms of real hypersurfaces, Amer. J. Math. 118 (1996), 209-233. MR 97h:32027
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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:
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
Copyright of article:
Copyright
1999,
American Mathematical Society
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