## Convergence and finite determination of formal CR mappings

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- by M. S. Baouendi, P. Ebenfelt and Linda Preiss Rothschild
- J. Amer. Math. Soc.
**13**(2000), 697-723 - DOI: https://doi.org/10.1090/S0894-0347-00-00343-X
- Published electronically: June 22, 2000
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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.## References

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## Bibliographic 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
- MR Author ID: 339422
- Email: ebenfelt@math.kth.se
**Linda Preiss Rothschild**- Affiliation: Department of Mathematics, 0112, University of California at San Diego, La Jolla, California 92093-0112
- MR Author ID: 151000
- Email: lrothschild@ucsd.edu
- 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.
- © Copyright 2000 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**13**(2000), 697-723 - MSC (2000): Primary 32H02
- DOI: https://doi.org/10.1090/S0894-0347-00-00343-X
- MathSciNet review: 1775734