Author

Zhi-Yuan Xu

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Preprint Oct 2026

Codimension Reduction of Minimal Submanifolds with Flat Normal Bundle in Spheres

Let $x:M^n\to\mathbb{S}^{n+q}$ be a minimal immersion of a complete connected manifold with flat normal bundle, where $n\ge3$ and $q\ge2$. We prove that if the squared norm of the second fundamental form $S$ satisfies $S<2n$, then $M^n$ lies in $\mathbb{S}^{n+1}$. The standard minimal products of three spheres show tha...

Juan Li, Zhi-Yuan Xu · 0 citations

Preprint Sep 2026

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...

Juan Li, Zhi-Yuan Xu · 0 citations