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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
Published electronically: September 30, 1999
MathSciNet review: 1646195
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Abstract: In this paper, we study noncompact complete Riemannian $n$-manifolds with $n\ge 3$ which are not pointwise conformal to subdomains of any compact Riemannian $n$-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

Keywords: Scalar curvature, Yamabe problem, conformal metric
Received by editor(s): July 22, 1998
Published electronically: 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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