Jianquan Ge

collaborators

13 papers

math.DG2026

Examples of Curvature Inhomogeneous Submanifolds with Constant Ricci Eigenvalues

Jianquan Ge, Yuyang Zhao

We construct two families of curvature inhomogeneous Riemannian manifolds with constant Ricci eigenvalues. The first, derived from the Einstein warped products, has two distinct Ri…

math.DG2026

Compactness and Willmore Energy of Helicoidal Minimal Surfaces in the 3-Sphere

Jianquan Ge, Shilin Li

The paper determines exactly when the helicoidal minimal surfaces Hel_c^h in the 3‑sphere are compact, showing this occurs for rational pitch values and an additional rationality c…

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

Sharp WeitzenbÃ¶ck and PIC2 Estimates from Sectional-Scalar Curvature Pinching

Jian Ge

Let $V$ be an $n$ -dimensional Euclidean vector space, ,where $n \geq 4$ , and $ℓ = ⌊ \frac{n}{2} ⌋$ . We prove the sharp pointwise estimate \[ q_2(E) \ge -\frac{2(\ell -1)…

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…