The skew mean curvature flow is an evolution equation for
In this article we propose a novel geometric model to study the motion of a physical flag. In our approach, a flag is viewed as an isometric immersion from the square with values in
 NSFPAR ID:
 10500851
 Publisher / Repository:
 Springer Science + Business Media
 Date Published:
 Journal Name:
 Archive for Rational Mechanics and Analysis
 Volume:
 248
 Issue:
 3
 ISSN:
 00039527
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract d dimensional manifolds embedded in (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 wellposedness in lowregularity Sobolev spaces for the skew mean curvature flow in dimension$${{\mathbb {R}}}^{d+2}$$ ${R}^{d+2}$ .$$d\ge 4$$ $d\ge 4$ 
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