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