A Model-threshold Dimension Bound and Sharp Critical Ends for Smooth Singular Sets of Constant Positive ${\sigma }_k$-curvature Metrics

Jiahuan Li, Yilu Liu, Xi-Nan Ma

Let $k\in \mathbb{N}$ satisfy $1<k<n/2$, and let $Σ^p\subset\Sn^n$ be a closed smooth embedded submanifold. We prove that a complete conformal metric $g=v^{-2}g_{\Sn^n}$ on $\Sn^n\se…