Mean Curvature flow in Higher Co-dimension

TL;DR

This paper advances the understanding of mean curvature flow in higher co-dimension by weakening key conditions for long-term existence and convergence, and introduces new applications.

Contribution

It improves previous results by relaxing curvature and lower bound conditions, expanding the applicability of mean curvature flow analysis.

Findings

Extended long-time existence results under weaker conditions

Proved convergence of solutions with relaxed assumptions

Introduced new applications of mean curvature flow in higher co-dimension

Abstract

We make several improvements on the results of M.-T. Wang in [8] and his joint paper with M.-P. Tsui [7] concerning the long time existence and convergence for solutions of mean curvature flow in higher co-dimension. Both the curvature condition and lower bound of $*\Omega$ are weakened. New applications are also obtained.