Surfaces of Co-dimension Two Pinched by Normal Curvature

TL;DR

This paper proves that certain codimension two surfaces with specific curvature conditions evolve smoothly into round points under mean curvature flow.

Contribution

It introduces a nonlinear curvature condition based on normal curvature and shows these surfaces deform to round points via mean curvature flow.

Findings

Surfaces with the specified curvature condition deform to round points.

The deformation process is smooth and well-behaved.

The result applies to a class of codimension two surfaces.

Abstract

We prove that codimension two surfaces satisfying a nonlinear curvature condition depending on normal curvature are smoothly deformed by mean curvature flow to round points.