Global Regularity of Schr��dinger Maps into the Hyperbolic Plane

It is about the global regularity of Schrödinger maps into the hyperbolic plane in dimensions greater than or equal to 3. In this book we show that the Schrödinger map initial-value problem into the hyperbolic plane admits a unique global-in-time smooth solution provided the initial value of the Schrödinger map has a small norm in some suitable space.