Weiran Ding

collaborators

8 papers

math.DG2026

A solution to a problem of Ghomi and Raffaelli on closed asymptotic curves

Weiran Ding

We construct a smooth embedded open annulus in Euclidean three-space with strictly negative Gaussian curvature and injective Gauss map that contains a simple closed asymptotic curv…

math.DG2026

A solution to Lu's second gap conjecture

Weiran Ding, Fagui Li, Xize Yang +1

Let $M^{n} \to S^{n + q} (1)$ be a closed connected minimal immersion, where $n \geq 3$ , and set $Q = S + λ_{2}$ , with $S = ∣ h ∣^{2}$ and $λ_{2}$ the second largest eigenvalue of Lu's fundamenta…

math.DG2026

A proof of the Simon conjecture and curvature rigidities

Weiran Ding, Jianquan Ge, Fagui Li

In this paper, we prove all gaps in the Simon conjecture for connected closed minimal surfaces immersed in unit spheres. Our proof uses the line-bundle ladder of Lin, Wang, and Xu…

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

On Simon's third gap conjecture for minimal surfaces in spheres

Weiran Ding, Jianquan Ge, Fagui Li

In this paper, continuing our previous work, we investigate the third gap problem in the Simon conjecture for closed minimal surfaces in the unit sphere. By developing refined thir…

math.DG2026

Lu's conjecture for minimal surfaces

Weiran Ding, Jianquan Ge, Fagui Li +1

After Chern's conjecture on the discreteness of the constant scalar curvatures of compact minimal submanifolds $M^{n}$ in unit spheres $S^{n + q}$ , Z. Q. Lu proposed a conject…

math.DG2024

Volume gap between the minimal submanifold and the unit sphere

Weiran Ding, Jianquan Ge, Fagui Li

In this paper, following the method of Cheng-Li-Yau, we first modify the coefficients in the constant $B_{n}$ to improve the volume gap. Further, we also enlarge our gap by applying…

math.DG2024

Pinching rigidity of minimal surfaces in spheres

Weiran Ding, Jianquan Ge, Fagui Li

In this paper we give a pinching theorem of the Simon conjecture in the case s=3 and also give a new proof of the cases s=1 and s=2 by some Simons-type integral inequalities.