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M. S. Baouendi P. Ebenfelt Linda Preiss Rothschild 《Journal of the American Mathematical Society》2000,13(4):697-723
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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We consider a Cauchy problem for an overdetermined system of nonlinear partial differential equations, and give necessary and sufficient conditions for solvability of this Cauchy problem for all data. As an application, we find all real tube hypersurfaces in complex space whose Levi number is maximal. 相似文献
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M. S. Baouendi et J. Sj?strand 《Arkiv f?r Matematik》1976,14(1):9-33
Sans résumé
Le premier auteur a bénéficié du “N.S.F. Grant 35 825”. 相似文献