Nowhere minimal CR submanifolds and Levi-flat hypersurfaces |
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Authors: | Jiří Lebl |
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Affiliation: | (1) Department of Mathematics, University of California at San Diego, 92093-0112 La Jolla, CA |
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Abstract: | A local uniqueness property of holomorphic functions on real-analytic nowhere minimal CR submanifolds of higher codimension is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being contained a possibly singular real-analytic Levi-flat hypersurface is studied and characterized. This question is completely resolved for algebraic submanifolds of codimension 2 and a sufficient condition for noncontainment is given for non algebraic submanifolds. As a consequence, an example of a submanifold of codimension 2, not biholomorphically equivalent to an algebraic one, is given. We also investigate the structure of singularities of Levi-flat hypersurfaces. |
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Keywords: | KeywordHeading" >Math Subject Classifications 32V40 32C07 |
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