Author

Qing-Ming Cheng

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Preprint Sep 2026

A Classification of Complete Self-shrinkers

Let $X:M^n\to\R^{n+1}$ be an $n$-dimensional complete self-shrinker. We obtain a complete classification of complete self-shrinkers with positive constant scalar curvature. More precisely, we prove that the round sphere $S^n(\sqrt n)$ and the standard generalized cylinder $S^k(\sqrt k)\times \R^{n-k}$ for $2\leq k\leq...

Qing-Ming Cheng, Feng-Jiang Li, Guo-Xin Wei · 1 citation

Preprint Oct 2026

An improved result on Chern conjecture

Let $X: M^n\to \mathbb S^{n+1}(1)$ be a closed minimal hypersurface with constant scalar curvature. Chern conjecture says that a closed minimal hypersurface with constant scalar curvature, $S\geq 2n$ if $S>n$, where $S$ is the squared norm of the second fundamental form. As a partial result, Peng-Terng \cite{pt1, pt2},...

Qing-Ming Cheng, Feng-Jiang Li, G. Wei · 0 citations