5 papers · 1 filter
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…
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…
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 in unit spheres , Z. Q. Lu proposed a conject…
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 to improve the volume gap. Further, we also enlarge our gap by applying…
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.