AbstractThe skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in $${{\mathbb {R}}}^{d+2}$$
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 $$d\ge 4$$
d
≥
4
.