An obstruction to the conformal compactification of Riemannian manifolds
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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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1833-1838
- MSC (1991): Primary 53C21; Secondary 58G30
- DOI: https://doi.org/10.1090/S0002-9939-99-05207-7
- MathSciNet review: 1646195