On the σκ -Nirenberg problem

Abstract

abstract: We consider the problem of prescribing the $\sigma_k$-curvature on the standard sphere $\Bbb{S}^n$ with $n\geq 3$. We prove existence and compactness theorems when $k\geq n/2$. This extends an earlier result of Chang, Han, and Yang for $n=4$ and $k=2$.