Convergence and finite determination of formal CR mappings

Baouendi, M.; Ebenfelt, P.; Rothschild, Linda

doi:10.1090/S0894-0347-00-00343-X

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.

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