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Convergence and finite determination of formal CR mappings


Authors: M. S. Baouendi, P. Ebenfelt and Linda Preiss Rothschild
Journal: J. Amer. Math. Soc. 13 (2000), 697-723
MSC (2000): Primary 32H02
DOI: https://doi.org/10.1090/S0894-0347-00-00343-X
Published electronically: June 22, 2000
MathSciNet review: 1775734
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Abstract: It is shown that a formal mapping between two real-analytic hypersurfaces in complex space is convergent provided that neither hypersurface contains a nontrivial holomorphic variety. For higher codimensional generic submanifolds, convergence is proved e.g. under the assumption that the source is of finite type, the target does not contain a nontrivial holomorphic variety, and the mapping is finite. Finite determination (by jets of a predetermined order) of formal mappings between smooth generic submanifolds is also established.


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Additional Information

M. S. Baouendi
Affiliation: Department of Mathematics, 0112, University of California at San Diego, La Jolla, California 92093-0112
Email: sbaouendi@ucsd.edu

P. Ebenfelt
Affiliation: Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Email: ebenfelt@math.kth.se

Linda Preiss Rothschild
Affiliation: Department of Mathematics, 0112, University of California at San Diego, La Jolla, California 92093-0112
Email: lrothschild@ucsd.edu

DOI: https://doi.org/10.1090/S0894-0347-00-00343-X
Keywords: Formal mappings, generic submanifolds, CR mappings, holomorphic mappings, finite determination
Received by editor(s): June 3, 1999
Published electronically: June 22, 2000
Additional Notes: The first and the third authors are partially supported by National Science Foundation grant DMS 98-01258. The second author is partially supported by a grant from the Swedish Natural Science Research Council.
Article copyright: © Copyright 2000 American Mathematical Society

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