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Igor G. Nikolaev Davis, Craig Charles 2015-09-28T15:19:35Z 2015-09-28T15:19:35Z 10000-01-01 2002 2002 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. http://hdl.handle.net/2142/86797 (MiAaPQ)AAI3070286 eng Mathematics Conformally Flat Spaces of Bounded Curvature text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.