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Vitushkin's Germ Theorem for Engel-Type CR Manifolds |
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MAIK Nauka - Interperiodica |
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10.1134/S0081543806020015 |
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| Abstract |
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We study real analytic CR manifolds of CR dimension 1 and codimension 2 in the three-dimensional complex space. We prove that the germ of a holomorphic mapping between 'nonspherical' manifolds can be extended along any path (this is an analog of Vitushkin's germ theorem). For a cubic model surface ('sphere'), we prove an analog of the Poincaré theorem on the mappings of spheres into ℂ². We construct an example of a compact 'spherical' submanifold in a compact complex 3-space such that the germ of a mapping of the 'sphere' into this submanifold cannot be extended to a certain point of the 'sphere'. |
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Proceedings of the Steklov Institute of Mathematics, 253(1), p. 1-7 |
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