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Tumanov, Alexander Scalari, Alberto 2015-09-28T15:19:29Z 2015-09-28T15:19:29Z 10000-01-01 2001 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. Made available in DSpace on 2015-09-28T15:19:29Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3017201.pdf: 2310876 bytes, checksum: 1310325f98d0091975d0a2437a2e4e52 (MD5) Previous issue date: 2001 Embargo set by: Seth Robbins for item 88059 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 55 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001. http://hdl.handle.net/2142/86778 (MiAaPQ)AAI3017201 eng Mathematics Extremal Discs and CR Geometry text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.