Complete conformal metrics with zero scalar curvature

Authors:
Xiaoyun Ma and Robert C. McOwen

Journal:
Proc. Amer. Math. Soc. **115** (1992), 69-77

MSC:
Primary 53C21; Secondary 35B40, 58G30

MathSciNet review:
1101988

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we consider the problem of when a noncompact Riemannian manifold admits a complete conformal metric with zero scalar curvature. In particular, we show that this can be achieved if is the noncompact manifold obtained by deleting a smooth submanifold from a compact Riemannian manifold provided and the Sobolev quotient is positive.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1992-1101988-1

Keywords:
Conformal metrics,
conformal Laplacian,
scalar curvature,
Riemannian manifolds

Article copyright:
© Copyright 1992
American Mathematical Society