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arXiv · 2608.16571

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
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Abstract

Let $k\in\mathbb N$ satisfy $1 0$ must obey \[ p\leq p_k(n), \] where $p_k$ is the model threshold determined by $\Hh^{p+1}\times\Sn^{n-p-1}$. When $k=2$ and $n=m^2$, we construct a smooth complete equality example on $\Sn^n\setminus\Sn^{(m^2-m-2)/2}$. We also prove that the strict inequality $p<p_k(n)$ holds under a finite positive linear-contact hypothesis.

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Jiahuan Li, Yilu Liu, Xi-Nan Ma. 2026-08-17. A Model-threshold Dimension Bound and Sharp Critical Ends for Smooth Singular Sets of Constant Positive $\sigma_k$-curvature Metrics. https://arxiv.org/abs/2608.16571

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