6 papers
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…
Weakly stable irreducible Yang-Mills fields over
Jianquan Ge, Lixin Xiao
Addressing Yau's conjecture (Problem 117) on , we investigate the self-duality of weakly stable Yang-Mills fields under the assumption of irreducibility. For structure groups…
Pinching rigidity theorems for normal scalar curvature
Jianquan Ge, Fagui Li, Yunheng Zhang
Let be an -dimensional closed minimal submanifold immersed in the unit sphere . Denote by and the squared norm of the second fundamental…
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.