The higher order Yamabe problem


Neil Trudinger (Australian National University and IAS)

Abstract:

The higher order Yamabe problem is to find a conformal metric, on an n-dimensional compact Riemannian manifold, with constant k - curvature, k = 2,3...n. Here the k-curvature is defined as the k-th elementary symmetric function of the eigenvalues of the Schouten tensor, with respect to the metric. We present recent work, in collaboration with Wei-min Sheng and Xu-jia Wang, on the solution of this problem and related issues such as the compactness of the solution set.