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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 Rd+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 .

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