Global Schr\"{o}dinger maps
  We consider the Schr\"{o}dinger map initial-value problem in dimension two or greater. We prove that the Schr\"{o}dinger map initial-value problem admits a unique global smooth solution, provided that the initial data is smooth and small in the critical Sobolev space. We prove also that the solution operator extends continuously to the critical Sobolev space. 
Ioan Bejenaru, Alexandru D. Ionescu, Carlos E. Kenig, Daniel Tataru