Global results for Schr\"odinger Maps in dimensions $n \geq 3$
  We study the global well-posedness theory for the Schr\"odinger Maps equation. We work in $n+1$ dimensions, for $n \geq 3$, and prove a local well-posedness for small initial data in $\dot{B}^{\frac{n}{2}}_{2,1}$. 
Ioan Bejenaru