Fagui Li

collaborators

11 papers

math.DG2026

Pinching rigidity of surfaces with parallel mean curvature vector in spheres

Weiran Ding, Jianquan Ge, Fagui Li

Inspired by the Simon conjecture for minimal surfaces in spheres, we study closed surfaces with parallel mean curvature vector and positive Gaussian curvature immersed in unit sphe…

math.DG2026

Lu's conjecture for minimal surfaces in codimension two

Jianquan Ge, Fagui Li, Yunheng Zhang

Let $M^{2} \to S^{4}$ be a closed minimal immersion, let $S$ be the squared norm of its second fundamental form, and let $I^»_{1} \geq I^»_{2} \geq 0$ be the eigenvalues of Lu's fundament…

math.DG2026

On Chern's Conjecture for Minimal Submanifolds with Flat Normal Bundle in Spheres

Jianquan Ge, Fagui Li, Yunheng Zhang

Let $M^{n}$ $(n ⩾ 3)$ be a closed minimal submanifold in the unit sphere $S^{n + m}$ $(m ⩾ 2)$ with flat normal bundle, and let $S$ denote the squared norm of its s…

math.DG2026

The Rigidity Theorems for Self-Shrinkers in the Mean Curvature Flow

Fagui Li, Yuhang Zhao

In this paper, we prove a spectral upper-pinching theorem for complete properly immersed self-shrinking hypersurfaces. Our argument is inspired by the second author's recent work\c…

math.DG2026

Flat minimal tori and Lu's second-gap conjecture

Fagui Li, Yuhang Zhao

Lu conjectured that, for each dimension and codimension, there exists a positive gap above the first pinching value for the quantity $S + λ_{2}$ on closed minimal submanifolds of the u…

math.DG2026

Gaussian-Weighted Curvature Gaps for Self-Shrinkers

Fagui Li, Yuhang Zhao

In this paper, we prove lower bounds for the Gaussian-weighted $L^2$-curvature integral of embedded self-shrinkers. The proof combines normal coordinate functions with weighted P…