Variational structure of the vn2-Yamabe problem

We define a formal Riemannian metric on a conformal class in the context of the vn2-Yamabe problem. We also give a new variational description of this problem, and show that the associated functional is geodesically convex. Formal properties of the negative gradient flow are also described. These results parallel our work in two dimensions on the Liouville energy and the uniformization of surfaces [14], and our work in four dimensions on the σ2-Yamabe problem [15].