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University of Illinois at Urbana-Champaign
Conformally Flat Spaces of Bounded Curvature
Abstract
dc:descriptionHere 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.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Davis, Craig Charles
- Contributors dc:contributor
-
- Igor G. Nikolaev
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI3070286
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86797