Extremal Discs and CR Geometry
type: CreativeWork
description: 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.
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.
author: Scalari, Alberto
language: eng
keywords: Mathematics
date published: 2015-09-28T15:19:29Z
date modified: 2026-07-22T22:26:27Z
provider: University of Illinois - Urbana-Champaign
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Illinois at Urbana-Champaign

PropertyValue
property ID: Handle
value: http://hdl.handle.net/2142/86778