Author

Wei-Ran Ding

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Preprint Sep 2026

A solution to Lu's second gap conjecture

Let $M^n\to\mathbb{S}^{n+q}(1)$ be a closed connected minimal immersion, where $n\ge3$, and set $Q=S+\lambda_2$, with $S=|h|^2$ and $\lambda_2$ the second largest eigenvalue of Lu's fundamental matrix. We determine the sharp codimension range for Lu's second-gap conjecture. For every $2\le q\le n$, there exists $\gamma...

Wei-Ran Ding, Fa-Gui Li, Xi-Ze Yang et al. · 0 citations

Preprint Sep 2026

On Lu's second gap conjecture in higher codimension

Let $M^n\to\Sph^{n+q}(1)$, $n\ge3$ and $q\ge2$, be a closed minimal immersion. Set $S=|h|^2$ and $Q=S+\lambda_2$, where $h$ is the second fundamental form and $\lambda_2$ is the second largest eigenvalue of Lu's fundamental matrix. We establish two complementary results concerning Lu's second-gap conjecture. First, for...

Wei-Ran Ding, Fa-Gui Li, Xi-Ze Yang et al. · 0 citations

Preprint Jul 2026

Pinching rigidity of surfaces with parallel mean curvature vector in spheres

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 spheres. Let $h$ be the second fundamental form, let $\mathbf{H}$ be the mean curvature vector field, and set $\tilde h=h-\mathbf{H}g$ and $\til...

Wei-Ran Ding, Jian-Quan Ge, Fa-Gui Li · 1 citation