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SEMIGLOBAL EXTENSION OF MAXIMALLY COMPLEX SUBMANIFOLDS

Part of: CR manifolds

Published online by Cambridge University Press:  13 July 2011

GIUSEPPE DELLA SALA  and
ALBERTO SARACCO
GIUSEPPE DELLA SALA
Affiliation:
Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, A-1090 Wien, Austria (email: giuseppe.dellasala@univie.ac.at)
ALBERTO SARACCO*
Affiliation:
Dipartimento di Matematica, Università di Parma, viale G. Usberti 53/A, I-43124 Parma, Italy (email: alberto.saracco@unipr.it)
*
✉For correspondence; e-mail: alberto.saracco@gmail.com
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Abstract

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Let A be a domain of the boundary of a (weakly) pseudoconvex domain Ω of ℂn and M a smooth, closed, maximally complex submanifold of A. We find a subdomain E of ℂn, depending only on Ω and A, and a complex variety W⊂E such that bW=M in E. Moreover, a generalization to analytic sets of depth at least 4 is given.

Keywords

boundary problempseudoconvexitymaximally complex submanifoldCR geometry

MSC classification

Secondary: 32V25: Extension of functions and other analytic objects from CR manifolds
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 3 , December 2011 , pp. 458 - 474
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

Giuseppe Della Sala has been partially supported by the BMWF grant Y377, Biholomorphic Equivalence: Analysis, Algebra and Geometry and Alberto Saracco has been supported by the MIUR Project Geometric Properties of Real and Complex Manifolds and by GNSAGA of INdAM.

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