Qingming Cheng

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20242026

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math.DG2026

A Classification of Complete Self-shrinkers

Qing-Ming Cheng, Fengjiang Li, Guoxin Wei

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 pr…

math.DG2026

Estimates on scalar curvature of self-shrinkers

Qing-Ming Cheng, Fengjiang Li, Guoxin Wei

In this paper, we study $n$ -dimensional complete self-shrinkers in $R^{n + 1}$ with constant squared norm $S$ of the second fundamental form. We partially resolve the conject…

math.DG2026

Examples of compact embedded mean convex $λ$ -hypersurfaces

Qing-Ming Cheng, Junqi Lai, Guoxin Wei

There is a well-known conjecture asserts that the round sphere should be the only compact embedded self-shrinker (i.e. $0$ -hypersurface) which is diffeomorphic to a sphere. S. Bren…

math.DG2025

Complete two-sided $δ$ -stable minimal hypersurfaces in $R^{n + 1}$

Qing-Ming Cheng, Guoxin Wei

In this paper, we study complete $δ$ -stable minimal hypersurfaces in $R^{n + 1}$ . We prove that complete two-sided $δ$ -stable minimal hypersurfaces have Euclidean volume grow…

math.DG2024

Embedded cylindrical and doughnut-shaped $λ$ -hypersurfaces

Qing-Ming Cheng, Junqi Lai, Guoxin Wei

In the paper, we construct, for $λ > 0$ , complete embedded and non-convex $λ$ -hypersurfaces, which are diffeomorphic to a cylinder. Hence, one can not expect that $λ$ -hypersurfaces s…

A Classification of Complete Self-shrinkers

Estimates on scalar curvature of self-shrinkers

Examples of compact embedded mean convex λ-hypersurfaces

Complete two-sided δ-stable minimal hypersurfaces in Rn+1

Embedded cylindrical and doughnut-shaped λ-hypersurfaces

Examples of compact embedded mean convex $λ$ -hypersurfaces

Complete two-sided $δ$ -stable minimal hypersurfaces in $R^{n + 1}$

Embedded cylindrical and doughnut-shaped $λ$ -hypersurfaces