The Intermediate Case of the Yamabe Problem for Higher Order Curvatures

In this paper, we prove the solvability, together with the compactness of the solution set, for the $\frac {n}{2}$ -Yamabe problem on compact Riemannian manifolds of arbitrary even dimension n > 2. These results had previously been obtained by Chang, Gursky, and Yang for the case n = 4 and by Li and Li for locally conformally flat manifolds in all even dimensions. Our proof also applies to more generally prescribed symmetric functions of the Ricci curvatures.