5 citations · 9 across the 22 of their papers we have counts for
25 papers
A Curvature Gap for Minimal Submanifolds in Spheres
Fagui Li, Yuhang Zhao
Let $F:M^n\to\Sn^{n+q}(1)$ be a closed minimal immersion in the unit sphere, with , . Let be the squared length of its second fundamental form. We prove that if $…
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…
Sphere Theorems for Immersed Hypersurfaces with Constant Scalar Curvature
Fagui Li
We prove sphere theorems for closed connected immersed hypersurfaces of constant scalar curvature in Euclidean space. Combining Ros's rigidity argument with the filling theorem of…
Conformal Boundary Deformations under Ricci Lower Bounds: Eigenvalue Counterexamples
Fagui Li, Yuhang Zhao
Let be a compact Riemannian manifold with boundary. Under the assumptions $\Ric_g\geq ng$ and $\II_g\geq0$, Wang proposed a sharp strengthening of the Choi--Wang--Rei…
Volume gap for minimal submanifolds in spheres, II
Jianquan Ge, Fagui Li
Let $f:M^n\looparrowright\Sph^{n+q}(1)$, and , be a closed, connected, non-totally-geodesic minimal immersion with second fundamental form , and put and…
The Rigidity Theorems for Self-Shrinkers in the Mean Curvature Flow
Fagui Li, Yuhang Zhao
In this paper, we prove a spectral upper-pinching theorem for complete properly immersed self-shrinking hypersurfaces. Our argument is inspired by the second author's recent work\c…
Lu's conjecture for minimal surfaces in codimension two
Jianquan Ge, Fagui Li, Yunheng Zhang
Let be a closed minimal immersion, let be the squared norm of its second fundamental form, and let be the eigenvalues of Lu's fundamental…
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 Chern's Conjecture for Minimal Submanifolds with Flat Normal Bundle in Spheres
Jianquan Ge, Fagui Li, Yunheng Zhang
Let be a closed minimal submanifold in the unit sphere with flat normal bundle, and let denote the squared norm of its s…
Gaussian-Weighted Curvature Gaps for Self-Shrinkers
Fagui Li, Yuhang Zhao
In this paper, we prove lower bounds for the Gaussian-weighted \(L^2\)-curvature integral of embedded self-shrinkers. The proof combines normal coordinate functions with weighted P…
Flat minimal tori and Lu's second-gap conjecture
Fagui Li, Yuhang Zhao
Lu conjectured that, for each dimension and codimension, there exists a positive gap above the first pinching value for the quantity on closed minimal submanifolds of the u…
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…
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.
A survey on the DDVV-type inequalities
Jianquan Ge, Fagui Li, Zizhou Tang +1
In this paper, we give a survey on the history and recent developments on the DDVV-type inequalities.
A first eigenvalue estimate for embedded hypersurfaces in positive Ricci curvature manifolds
Fagui Li, Junrong Yan
Let be a closed, embedded, oriented hypersurface in a closed oriented Riemannian manifold . Under a lower bound on the Ricci curvature and an upper bound on the sectional cu…
Volume gap for minimal submanifolds in spheres
Jianquan Ge, Fagui Li
For a closed minimal submanifold in the unit sphere , we prove $${\rm Vol}(M^n) \geq\frac{n+1}{n+2}\int_{M}\left( 1+φ_{p}^2\right) \geq…
An isoperimetric inequality of minimal hypersurfaces in spheres
Fagui Li, Niang Chen
Let be a closed immersed minimal hypersurface in the unit sphere . We establish a special isoperimetric inequality of . As an application, if the scal…
A note on the Chern Conjecture in dimension four
Fagui Li
Let be a closed immersed minimal hypersurface with constant squared length of the second fundamental form and constant 3-mean curvature in . If $H_3…
A lower bound for length of second fundamental form on minimal hypersurfaces
Jianquan Ge, Fagui Li
We prove a weak version of the Perdomo Conjecture, namely, there is a positive constant depending only on such that on any closed embedded, non-totally geodesic, minim…
Integral-Einstein hypersurfaces in spheres
Jianquan Ge, Fagui Li
Combining the intrinsic and extrinsic geometry, we generalize Einstein manifolds to Integral-Einstein (IE) submanifolds. A Takahashi-type theorem is established to characterize min…
On some conjectures by Lu and Wenzel
Jianquan Ge, Fagui Li, Zhiqin Lu +1
In order to give a unified generalization of the BW inequality and the DDVV inequality, Lu and Wenzel proposed three Conjectures 1, 2, 3 and an open Question 1 in 2016. In this pap…