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On the Hans Lewy extension phenomenon in higher codimension


Authors: C. D. Hill and G. Taiani
Journal: Proc. Amer. Math. Soc. 91 (1984), 568-572
MSC: Primary 32D15; Secondary 32F30
MathSciNet review: 746091
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Abstract: In this work the authors extend the results of their paper entitled Families of analytic discs in $ {{\mathbf{C}}^n}$ with boundaries on a prescribed $ CR$ submanifold. It is proven that a nongeneric CR manifold $ M$ whose Lewy form is not identically zero can be extended to a manifold $ \tilde M$ of one higher dimension, which is foliated by analytic discs. Moreover this result is used to prove that a sufficiently smooth CR function $ f$ on $ M$ extends to a function $ \tilde f$ which is CR on $ \tilde M$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0746091-0
Article copyright: © Copyright 1984 American Mathematical Society