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 Title: Conformally Flat Spaces of Bounded Curvature Author(s): Davis, Craig Charles Doctoral Committee Chair(s): Igor G. Nikolaev Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics 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. Issue Date: 2002 Type: Text Language: English Description: 98 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002. URI: http://hdl.handle.net/2142/86797 Other Identifier(s): (MiAaPQ)AAI3070286 Date Available in IDEALS: 2015-09-28 Date Deposited: 2002
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