Complete conformal metrics with zero scalar curvature

Ma, Xiaoyun; McOwen, Robert C.

doi:10.1090/S0002-9939-1992-1101988-1

Complete conformal metrics with zero scalar curvature
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by Xiaoyun Ma and Robert C. McOwen PDF

Proc. Amer. Math. Soc. 115 (1992), 69-77 Request permission

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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