20 citations · 115 across the 45 of their papers we have counts for
50 papers
Collapse to nonsmoothable manifolds under lower sectional and positive Ricci curvature bounds
Jian Ge, Chao Qian
We construct smooth collapsing sequences with sectional curvature at least whose limits are topological manifolds with nonzero Kirby--Siebenmann class. For every , the…
Total scalar curvature under a curvature operator lower bound
Jian Ge, Chuanhuan Li, Ronggang Li
Let be a complete, simply connected Riemannian manifold without boundary, of dimension , with curvature operator at least that of the unit sphere. We prove that…
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…
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…
Almost Nonnegative Ricci curvature and new vanishing theorems for genera
Xiaoyang Chen, Jian Ge, Fei Han
We derive several vanishing theorems for genera under almost nonnegative Ricci curvature and infinite fundamental group, which includes Todd genus, -genus, elliptic ge…