23 citations · 56 across the 21 of their papers we have counts for
21 papers
Topological classification of Bazaikin spaces
Fuquan Fang, Wen Shen
Geometry of manifolds with positive sectional curvature has been a central object dates back to the beginning of Riemannian geometry. Up to homeomorphism, there are only finitely m…
Isoperimetric Bounds for Lower Order Eigenvalues
Fuquan Fang, Changyu Xia
New isoperimetric inequalities for lower order eigenvalues of the Laplacian on closed hypersurfaces, of the biharmonic Steklov problems and of the Wentzell-Laplace on bounded domai…
Dual submanifolds in rational homology spheres
Fuquan Fang
Let be a simply connected rational homology sphere. A pair of disjoint closed submanifolds in are called dual to each other if the complement strongly h…
Rank three geometry and positive curvature
Fuquan Fang, Karsten Grove, Gudlaugur Thorbergsson
An axiomatic characterization of buildings of type $\CC_3$ due to Tits is used to prove that any cohomogeneity two polar action of type $\CC_3$ on a positively curved simply connec…
An almost flat manifold with a cyclic or quaternionic holonomy group bounds
James F. Davis, Fuquan Fang
A long-standing conjecture of Farrell and Zdravkovska and independently S.~T.~Yau states that every almost flat manifold is the boundary of a compact manifold. This paper gives a s…
Reflection groups in non-negative curvature
Fuquan Fang, Karsten Grove
We provide an equivariant description/classification of all complete (compact or not) non-negatively curved manifolds M together with a co-compact action by a reflection group W, a…