Local well-posedness of skew mean curvature flow for small data in $d\ge 4$ dimensions

Abstract

The skew mean curvature flow is an evolution equation for $d$ dimensional manifolds embedded in ${\mathbb{R}}^{d+2}$ (or more generally, in a Riemannian manifold). It can be viewed as a Schrödinger analogue of the mean curvature flow, or alternatively as a quasilinear version of the Schrödinger Map equation. In this article, we prove small data local well-posedness in low-regularity Sobolev spaces for the skew mean curvature flow in dimension $d\ge 4$.

References in corpus (1)

• Quasilinear Schrödinger equations III: Large Data and Short Time