The Yamabe problem on subdomains of even-dimensional spheres - Pacard, Frank (Topological Methods in Nonlinear Analysis, 1995)
We prove the existence of completeconformally flat metrics of constant positive scalar curvature on thecomplement in ${\mathbb S}^n$ of a finite number of $(n-2)/2$-dimensionalsmooth submanifolds, provided $n ≥ 4$ is even.