{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86778"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86778","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Extremal Discs and CR Geometry","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.","abstract_html":"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_has_math":false,"creators":["Scalari, Alberto"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Tumanov, Alexander"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:29Z","date_published":"2015-09-28T15:19:29Z","updated_at":"2026-07-22T22:26:27Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3017201"],"render_values":[{"text":"(MiAaPQ)AAI3017201","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86778","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Tumanov, Alexander"]},{"key":"dc:creator","label":"Author","values":["Scalari, Alberto"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:29Z","10000-01-01","2001"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86778","(MiAaPQ)AAI3017201"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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."]},{"key":"dc:title","label":"Title","values":["Extremal Discs and CR Geometry"]}]}],"canonical_facts":{"dc:contributor":["Tumanov, Alexander"],"dc:creator":["Scalari, Alberto"],"dc:date":["2015-09-28T15:19:29Z","10000-01-01","2001"],"dc: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.","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."],"dc:identifier":["http://hdl.handle.net/2142/86778","(MiAaPQ)AAI3017201"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["Extremal Discs and CR Geometry"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:27Z"}