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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the Schwarz symmetry principle in a model case
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by Joël Merker and Francine Meylan PDF
Proc. Amer. Math. Soc. 127 (1999), 1097-1102 Request permission

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
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  • M. S. Baouendi and Linda Preiss Rothschild, Germs of CR maps between real analytic hypersurfaces, Invent. Math. 93 (1988), no. 3, 481–500. MR 952280, DOI 10.1007/BF01410197
  • S. Baouendi, X. Huang and L. Rothschild, Regularity of CR mappings between algebraic hypersurfaces, Invent. Math. 125 (1996), 13-36.
  • 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
  • Francine Meylan, A reflection principle in complex space for a class of hypersurfaces and mappings, Pacific J. Math. 169 (1995), no. 1, 135–160. MR 1346250, DOI 10.2140/pjm.1995.169.135
  • F. Meylan and H.-M. Maire, Extension of smooth CR mappings between non essentially finite hypersurfaces in $\mathbb {C}^3$, Ark. Mat. 35 (1997), 185-199.
  • N. Mir, An algebraic characterization of holomorphic degeneracy and analyticity of CR mappings, Preprint, 1997.
  • Nancy K. Stanton, Infinitesimal CR automorphisms of real hypersurfaces, Amer. J. Math. 118 (1996), no. 1, 209–233. MR 1375306, DOI 10.1353/ajm.1996.0005
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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
  • MR Author ID: 355901
  • Email: meylan@unifr.ch
  • 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 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 1097-1102
  • MSC (1991): Primary 32H02; Secondary 32C05, 32C16
  • DOI: https://doi.org/10.1090/S0002-9939-99-04688-2
  • MathSciNet review: 1476379