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

2020/07/14 by Ze Li, Li, Ze
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.2007.07007

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.

Citations

• The General Quasilinear Ultrahyperbolic Schrödinger Equation

Related

• Global and local theory of skew mean curvature flows
• Global regularity of Skew mean curvature flow for small data in d≥ 4 dimensions
• Skew Mean Curvature Flow
• Stability of the surface area preserving mean curvature flow in Euclidean space
• Stability of translating solutions to mean curvature flow