  A refined trilinear Strichartz estimate for solutions to the Schr\"odinger
equation on the flat rational torus T^3 is derived. By a suitable modification
of critical function space theory this is applied to prove a small data global
well-posedness result for the quintic Nonlinear Schr\"odinger Equation in
H^s(T^3) for all s \geq 1. This is the first energy-critical global
well-posedness result in the setting of compact manifolds.

Analysis of PDEs