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 | References | Similar Articles | Additional Information

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