Global regularity of Skew mean curvature flow for small data in $d\ge 4$ dimensions

Abstract

The skew mean curvature flow is an evolution equation for a $d$ dimensional manifold immersed into ${\mathbb{R}}^{d+2}$, and which moves along the binormal direction with a speed proportional to its mean curvature. In this article, we prove small data global regularity in low-regularity Sobolev spaces for the skew mean curvature flow in dimensions $d\ge 4$. This extends the local well-posedness result in \cite{HT}.

38 pages