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Bishop, Richard L. Kim, Seongtag 2011-05-07T12:30:48Z 2011-05-07T12:30:48Z 10000-01-01 1994 Let (M,g) be a noncompact complete Riemannian manifold whose scalar curvature S(x) is positive for all x in M. In this thesis, we study a conformal deformation of the given metric g, which makes the scalar curvature of the deformed metric a positive constant. We also study the existence of a complete conformal metric with positive constant scalar curvature. We obtain a sufficient condition for the existence of a conformal metric with positive constant scalar curvature by studying the conformal structure at infinity. To study the existence of a complete solution, we calculate the Sobolev Quotient on a special admissible set whose elements are candidates for complete solutions. By studying the conformal structure at infinity, the behavior of scalar curvature and the Ricci curvatue in radial direction, we also obtain a sufficient condition for the existence of a complete conformal metric with positive constant scalar curvature. This study finds an interesting obstruction for the existence of an injective conformal immersion from the given m-dimensional complete Riemannian manifold to an m-dimensional compact Riemannian manifold. Made available in DSpace on 2011-05-07T12:30:48Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9503236.pdf: 1499151 bytes, checksum: 6bd7cd3be7126bf1c4a73c2282972432 (MD5) Previous issue date: 1994 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:41:59Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:18:14-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9503236 (UMI)AAI9503236 http://hdl.handle.net/2142/20163 eng Copyright 1994 Kim, Seongtag Mathematics Scalar curvature on noncompact complete Riemannian manifolds text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.