14 citations · 89 across the 29 of their papers we have counts for
6 papers · 1 filter
Topological and differentiable rigidity of submanifolds in space forms
Hong-Wei Xu, Juan-Ru Gu
Let be an -dimensional simply connected space form with nonnegative constant curvature . We prove that if is a compact submanifold in $F^{n+p}(…
Mean Curvature Flow of Higher Codimension in Hyperbolic Spaces
Kefeng Liu, Hongwei Xu, Fei Ye +1
In this paper we investigate the convergence for the mean curvature flow of closed submanifolds with arbitrary codimension in space forms. Particularly, we prove that the mean curv…
Rigidity of submanifolds with parallel mean curvature in space froms
Hong-Wei Xu, Juan-Ru Gu
Let be an -dimensional oriented compact submanifold with parallel mean curvature in the simply connected space form with , where is the mean…
The extension and convergence of mean curvature flow in higher codimension
Kefeng Liu, Hongwei Xu, Fei Ye +1
In this paper, we first investigate the integral curvature condition to extend the mean curvature flow of submanifolds in a Riemannian manifold with codimension , which gen…
On Yau rigidity theorem for minimal submanifolds in spheres
Juan-Ru Gu, Hong-Wei Xu
In this note, we investigate the well-known Yau rigidity theorem for minimal submanifolds in spheres. Using the parameter method of Yau and the DDVV inequality verified by Lu, Ge a…
The sphere theorems for manifolds with positive scalar curvature
Juan-Ru Gu, Hong-Wei Xu
Some new differentiable sphere theorems are obtained via the Ricci flow and stable currents. We prove that if is a compact manifold whose normalized scalar curvature and sect…