The axisymmetric ${\sigma }_k$-Nirenberg problem

Yanyan Li, Luc Nguyen, Bo Wang

We study the problem of prescribing ${\sigma }_k$-curvature for a conformal metric on the standard sphere ${\mathbb{S}}^n$ with $2\le k<n/2$ and $n\ge 5$ in axisymmetry. Compactness, n…