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https://hdl.handle.net/2142/86778
Description
Title
Extremal Discs and CR Geometry
Author(s)
Scalari, Alberto
Issue Date
2001
Doctoral Committee Chair(s)
Tumanov, Alexander
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
This thesis covers two results: (1) A determination of the dimension of the set of extremal discs attached to a CR strictly pseudoconvex manifold of codimension two in C 4: we prove that, for such a manifold, extremal discs depend on 15 parameters, one more than the parameters needed to describe extremal discs attached to a quadric. We point out some consequences. (2) A continuation result for a CR map. Let M be an analytic, strictly pseudoconvex, connected, generic manifold with generating Levi form, of codimension two in C 4. Let U be an open set in M. We prove that a real analytic diffeomorphic CR map from U to an open set in S 3 x S 3, extends as a real analytic locally diffeomorphic CR map on the whole manifold M. This provides a generalization of the notion of spherical manifolds, introduced by Pinchuk [P2] for hypersurfaces, to the case of codimension 2.
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