{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86797"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86797","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Conformally Flat Spaces of Bounded Curvature","abstract":"Here we show that if the logarithm of the conformal factor is subharmonic then the space has curvature bounded above by zero, and, subject to a growth constraint, if the logarithm of the conformal factor is subharmonic under all conformal transformations then the curvature is bounded below by zero. If the space has Lipschitz conformal factor and curvature bounded below by zero then the two dimensional subspaces have curvature bounded below by K, depending only on the Lipschitz constant and the size of the function.","abstract_html":"Here we show that if the logarithm of the conformal factor is subharmonic then the space has curvature bounded above by zero, and, subject to a growth constraint, if the logarithm of the conformal factor is subharmonic under all conformal transformations then the curvature is bounded below by zero. If the space has Lipschitz conformal factor and curvature bounded below by zero then the two dimensional subspaces have curvature bounded below by K, depending only on the Lipschitz constant and the size of the function.","abstract_has_math":false,"creators":["Davis, Craig Charles"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Igor G. Nikolaev"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:35Z","date_published":"2015-09-28T15:19:35Z","updated_at":"2026-07-22T22:26:27Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3070286"],"render_values":[{"text":"(MiAaPQ)AAI3070286","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86797","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Igor G. Nikolaev"]},{"key":"dc:creator","label":"Author","values":["Davis, Craig Charles"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:35Z","10000-01-01","2002"]},{"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/2142/86797","(MiAaPQ)AAI3070286"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Here we show that if the logarithm of the conformal factor is subharmonic then the space has curvature bounded above by zero, and, subject to a growth constraint, if the logarithm of the conformal factor is subharmonic under all conformal transformations then the curvature is bounded below by zero. If the space has Lipschitz conformal factor and curvature bounded below by zero then the two dimensional subspaces have curvature bounded below by K, depending only on the Lipschitz constant and the size of the function.","Made available in DSpace on 2015-09-28T15:19:35Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3070286.pdf: 3614441 bytes, checksum: 9979a8c4d603fcf2eff327362d68891b (MD5) Previous issue date: 2002","Embargo set by: Seth Robbins for item 88078 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","98 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002."]},{"key":"dc:title","label":"Title","values":["Conformally Flat Spaces of Bounded Curvature"]}]}],"canonical_facts":{"dc:contributor":["Igor G. Nikolaev"],"dc:creator":["Davis, Craig Charles"],"dc:date":["2015-09-28T15:19:35Z","10000-01-01","2002"],"dc:description":["Here we show that if the logarithm of the conformal factor is subharmonic then the space has curvature bounded above by zero, and, subject to a growth constraint, if the logarithm of the conformal factor is subharmonic under all conformal transformations then the curvature is bounded below by zero. If the space has Lipschitz conformal factor and curvature bounded below by zero then the two dimensional subspaces have curvature bounded below by K, depending only on the Lipschitz constant and the size of the function.","Made available in DSpace on 2015-09-28T15:19:35Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3070286.pdf: 3614441 bytes, checksum: 9979a8c4d603fcf2eff327362d68891b (MD5) Previous issue date: 2002","Embargo set by: Seth Robbins for item 88078 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","98 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002."],"dc:identifier":["http://hdl.handle.net/2142/86797","(MiAaPQ)AAI3070286"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["Conformally Flat Spaces of Bounded Curvature"],"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"}