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An obstruction to the conformal compactification of Riemannian manifolds
Author:
Seongtag Kim
Journal:
Proc. Amer. Math. Soc. 128 (2000), 1833-1838
MSC (1991):
Primary 53C21; Secondary 58G30
Posted:
September 30, 1999
MathSciNet review:
1646195
Full-text PDF Free Access
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Abstract: In this paper, we study noncompact complete Riemannian  -manifolds with  which are not pointwise conformal to subdomains of any compact Riemannian  -manifold. For this, we compare the Sobolev Quotient at infinity of a noncompact complete Riemannian manifold with that of the singular set in a compact Riemannian manifold using the method for the Yamabe problem.
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Additional Information
Seongtag Kim
Affiliation:
Department of Mathematics, Sungkyunkwan University, Suwon 440-746, South Korea
Email:
stkim@yurim.skku.ac.kr
DOI:
http://dx.doi.org/10.1090/S0002-9939-99-05207-7
PII:
S 0002-9939(99)05207-7
Keywords:
Scalar curvature,
Yamabe problem,
conformal metric
Received by editor(s):
July 22, 1998
Posted:
September 30, 1999
Additional Notes:
The author was supported in part by KOSEF96070102013 and BSRI 97-1419 Ministry of Education.
Communicated by:
Christopher Croke
Article copyright:
© Copyright 2000 American Mathematical Society
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