Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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: In this paper we consider the problem of when a noncompact Riemannian manifold $ \widehat{M}$ admits a complete conformal metric with zero scalar curvature. In particular, we show that this can be achieved if $ \widehat{M}$ is the noncompact manifold obtained by deleting a smooth submanifold $ {\Gamma ^n}$ from a compact Riemannian manifold $ {M^N}$ provided $ n \leq (N - 2)/2$ and the Sobolev quotient is positive.

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Keywords: Conformal metrics, conformal Laplacian, scalar curvature, Riemannian manifolds
Article copyright: © Copyright 1992 American Mathematical Society