On the ${\sigma }_k$-Nirenberg problem

Abstract

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

Accepted version. To appear in American Journal of Mathematics

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Cited by in corpus (2)

• Local pointwise second derivative estimates for strong solutions to the ${\sigma }_k$-Yamabe equation on Euclidean domains
• Compactness Theorem of Complete k-Curvature Manifolds with Isolated Singularities