### The Yamabe problem on subdomains of even-dimensional spheres

DOI: http://dx.doi.org/10.12775/TMNA.1995.036

#### Abstract

We prove the existence of complete

conformally flat metrics of constant positive scalar curvature on the

complement in ${\mathbb S}^n$ of a finite number of $(n-2)/2$-dimensional

smooth submanifolds, provided $n \geq 4$ is even.

conformally flat metrics of constant positive scalar curvature on the

complement in ${\mathbb S}^n$ of a finite number of $(n-2)/2$-dimensional

smooth submanifolds, provided $n \geq 4$ is even.

#### Keywords

conformally flat metrics; constant positive curvature; existence theorem; Yamabe problem

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