Global well-posedness and scattering for the defocusing mass-critical nonlinear Schrödinger equation for radial data in high dimensions

We establish global well-posedness and scattering for solutions to the defocusing mass-critical (pseudoconformal) nonlinear Schrodinger equation ¨ iut +
u =|u|4/nu for large, spherically symmetric, L^2x (Rn) initial data in dimensions n ≥ 3. After using the concentration-compactness reductions in [32] to reduce to eliminating blow-up solutions that are almost periodic modulo scaling, we obtain a frequency-localized Morawetz estimate and exclude a mass evacuation scenario (somewhat analogously to [10], [23], [36]) in order to conclude the argument