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In this paper, we study the skew mean curvature flow. The results arethreefold. First, we prove the global regularity of solutions with initial datawhich are small perturbations of planes in Sobolev spaces. Second, we prove themodified scattering and the existence of wave operators for small data, whichcompletely determines the set of asymptotic states. Third, we study the Cauchyproblem for arbitrary large data.

Global and local theory of skew mean curvature flows