4 papers
Conjugate radius of open manifolds
Jian Ge, Shimeng Zhang
In this short note, we establish an upper bound for the conjugate radius of an open -dimensional Riemannian manifold under a scalar curvature lower bound and a bottom-of-spectru…
Austere Matrices, Austere Submanifolds and Dupin Hypersurfaces
Jianquan Ge, Yi Zhou
Motivated by Bryant's research on austere subspaces and Cartan's isoparametric hypersurfaces with 3 distinct principal curvatures, we construct three families of austere submanifol…
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…
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+Ï_{p}^2\right) \ge…