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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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