I will discuss some recent joint work with Matt Gursky, where we consider the problem of conformally deforming a metric to prescribed symmetric function of the eigenvalues of the Schouten tensor. This is also known as the sigma_k-Yamabe problem. The Yamabe problem for the scalar curvature corresponds to \(k=1\), which is a semilinear equation. However, for \(k > 1\), the equation is fully nonlinear, so requires new techniques.

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