Global transversal stability of Euclidean planes under skew mean curvature flow evolutions

TL;DR

This paper proves that small transversal perturbations of Euclidean planes under skew mean curvature flow result in global solutions that converge back to the original planes, with detailed analysis of their long-term behavior in Sobolev spaces.

Contribution

It establishes the global stability and convergence of Euclidean planes under skew mean curvature flow for small transversal perturbations, clarifying their long-time dynamics.

Findings

Global solutions exist for small transversal perturbations.

Solutions converge to the original planes over time.

Long-term behavior analyzed in Sobolev spaces.

Abstract

In this paper, we prove that 2 dimensional transversal small perturbations of d-dimensional Euclidean planes under the skew mean curvature flow lead to global solutions which converge to the unperturbed planes in suitable norms. And we clarify the long time behaviors of the solutions in Sobolev spaces.