Local Well-Posedness of Skew Mean Curvature Flow for Small Data in d ≥ 4 Dimensions.

The skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in 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 ≥ 4 .