Mean curvature flow via convex functions on Grassmannian manifolds

TL;DR

This paper extends interior estimates for mean curvature flow to higher codimension by utilizing convex functions on Grassmannian manifolds, generalizing previous results by Ecker and Huisken.

Contribution

It introduces a novel approach using convex functions on Grassmannian manifolds to analyze mean curvature flow in higher codimension, broadening the scope of existing techniques.

Findings

Generalized interior estimates for higher codimension mean curvature flow

Established a new method using convex functions on Grassmannian manifolds

Extended results of Ecker-Huisken to more complex settings

Abstract

Using the convex functions in Grassmannian manifolds we can carry out interior estimates for mean curvature flow of higher codimension. In this way some of the results of Ecker-Huisken can be generalized to higher codimension