Global Well-posedness of the Energy-Critical Defocusing NLS on Rectangular Tori in three Dimensions

The energy-critical defocusing nonlinear Schr"odinger equation on 3-dimensional rectangular tori is considered. We prove that the global well-posedness result for the standard torus of Ionescu and Pausader extends to this class of manifolds, namely, for any initial data in $H^1$ the solution exists globally in time.