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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Convergence and finite determination of formal CR mappings
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by M. S. Baouendi, P. Ebenfelt and Linda Preiss Rothschild PDF
J. Amer. Math. Soc. 13 (2000), 697-723 Request permission

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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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
  • 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