Mean curvature flow of arbitrary codimension in spheres and sharp differentiable sphere theorem

Abstract

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 the convergence theorem of Baker [2] as well as the differentiable sphere theorems of Gu-Xu-Zhao [16, 50, 52].

21 pages

References in corpus (5)

• Positively curved surfaces in the three-sphere
• Lectures on mean curvature flows in higher codimensions
• Mean curvature flow of higher codimension in Riemannian manifolds
• An Optimal Convergence Theorem for Mean Curvature Flow of Arbitrary Codimension in Hyperbolic Spaces
• A New Version of Huisken's Convergence Theorem for Mean Curvature Flow in Spheres

Cited by in corpus (4)

• New Developments in Mean Curvature Flow of Arbitrary Codimension Inspired By Yau Rigidity Theory
• Ancient Solution of Mean Curvature Flow in Space Forms
• Surfaces pinched by normal curvature for mean curvature flow in space forms
• A sharp convergence theorem for the mean curvature flow in spheres I