Mean curvature flow with flat normal bundles

TL;DR

This paper proves that flatness of the normal bundle remains intact during mean curvature flow in Euclidean space and extends classical hypersurface results to submanifolds of higher codimension.

Contribution

It establishes the preservation of normal bundle flatness under mean curvature flow and generalizes a key hypersurface result to higher codimension submanifolds.

Findings

Normal bundle flatness is preserved during mean curvature flow.

Generalization of Ecker-Huisken's classical result to higher codimension.

Provides new insights into submanifold evolution in Euclidean space.

Abstract

We show that flatness of the normal bundle is preserved under the mean curvature flow in the Euclidean space and use this to generalize a classical result for hypersurfaces due to Ecker-Huisken in the case of submanifolds with arbitrary codimension.