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arXiv · 2605.18532

Estimates on scalar curvature of self-shrinkers

Qing-Ming Cheng·Fengjiang Li·Guoxin Wei
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Abstract

In this paper, we study $n$-dimensional complete self-shrinkers in $\mathbb R^{n+1}$ with constant squared norm $S$ of the second fundamental form. We partially resolve the conjecture on $n$-dimensional complete self-shrinkers in $\mathbb R^{n+1}$ with constant squared norm $S$ of the second fundamental form. Furthermore, if the scalar curvature of an $n$-dimensional self-shrinker is constant, then we prove that the scalar curvature $R$ satisfies $R\leq n-1$. We also classify $n$-dimensional complete self-shrinkers in $\mathbb R^{n+1}$ with non-negative constant scalar curvature.

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Qing-Ming Cheng, Fengjiang Li, Guoxin Wei. 2026-05-18. Estimates on scalar curvature of self-shrinkers. https://arxiv.org/abs/2605.18532

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