Zhi-Yuan Xu

Rigidity of Ricci-Pinched Complete Self-Shrinkers in Arbitrary Codimension

Let $M$ be an $n$-dimensional complete connected self-shrinker in $\mathbb{R}^{n+p}$. Denote by $\operatorname{Ric}$ and $\mathbf{H}$ the Ricci curvature tensor and the mean curvature vector of $M$, respectively. We prove that if the self-shrinker $M$ satisfies $\operatorname{Ric}\ge(\frac{n-2}{n^2}+\varepsilon_n)|\mat...