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Convergence and finite determination of formal CR mappings

M. S. Baouendi·P. Ebenfelt·L. P. Rothschild
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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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M. S. Baouendi, P. Ebenfelt, L. P. Rothschild. 1999-04-16. Convergence and finite determination of formal CR mappings. https://arxiv.org/abs/math/9904085

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