Surfaces pinched by normal curvature for mean curvature flow in space forms

Abstract

In this paper, we investigate the mean curvature flow of compact surfaces in $4$-dimensional space forms. We prove the convergence theorems for the mean curvature flow under certain pinching conditions involving the normal curvature, which generalise Baker-Nguyen's convergence theorem.

References in corpus (5)

• Normal scalar curvature conjecture and its applications
• Lectures on mean curvature flows in higher codimensions
• Mean curvature flow of arbitrary codimension in spheres and sharp differentiable sphere theorem
• An Optimal Convergence Theorem for Mean Curvature Flow of Arbitrary Codimension in Hyperbolic Spaces
• New Developments in Mean Curvature Flow of Arbitrary Codimension Inspired By Yau Rigidity Theory

Cited by in corpus (1)

• On the mean curvature flow of submanifolds in the standard Gaussian space ${}^{†}$