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 Schr\odinger analogue of the mean curvature flow, or alternatively as a quasilinear version of the Schr\odinger Map equation. In this talk, we will discuss the global well-posedness in Sobolev spaces for skew mean curvature flow. This is based on joint work with Ze Li and Daniel Tataru.

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