On the σ 2-Nirenberg problem on S 2

We establish theorems on the existence and compactness of solutions to the σ 2 -Nirenberg problem on the standard sphere S 2 . A first significant ingredient, a Liouville type theorem for the associated fully nonlinear Möbius invariant elliptic equations, was established in an earlier paper of ours. Our proof of the existence and compactness results requires a number of additional crucial ingredients which we prove in this paper: A Liouville …