Extremal Discs and CR Geometry

55 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.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.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD