Global well-posedness of the energy-critical nonlinear Schrödinger equation with small initial data in H1(T3)

A refined trilinear Strichartz estimate for solutions to the Schrödinger equation on the flat rational torus T3 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 Schrödinger equation in Hs(T3) for all s≥1. This is the first energy-critical global well-posedness result in the setting of compact manifolds.