14 citations · 89 across the 29 of their papers we have counts for
4 papers · 1 filter
An Eigenvalue Pinching Theorem for Compact Hypersurfaces in A Sphere
Yingxiang Hu, Hongwei Xu
In this article, we prove an eigenvalue pinching theorem for the first eigenvalue of the Laplacian on compact hypersurfaces in a sphere. Let be a closed, connected and or…
A New Version of Huisken's Convergence Theorem for Mean Curvature Flow in Spheres
Li Lei, Hongwei Xu
We prove that if the initial hypersurface of the mean curvature flow in spheres satisfies a sharp pinching condition, then the solution of the flow converges to a round point or a…
Mean curvature flow of arbitrary codimension in spheres and sharp differentiable sphere theorem
Li Lei, Hongwei Xu
In this paper, we investigate Liu-Xu-Ye-Zhao's conjecture [30] and prove a sharp convergence theorem for the mean curvature flow of arbitrary codimension in spheres which improves…
An Optimal Convergence Theorem for Mean Curvature Flow of Arbitrary Codimension in Hyperbolic Spaces
Li Lei, Hongwei Xu
In this paper, we prove that if the initial submanifold of dimension satisfies an optimal pinching condition, then the mean curvature flow of arbitrary codimension…