On the classification of minimal mass blowup solutions of the focusing mass-critical Hartree equation

Consider the focusing mass-critical nonlinear Hartree equation iut+Δu=−(−2|⋅|∗2|u|)u for spherically symmetric initial data with ground state mass M(Q) in dimension d⩾5. We show that any global solution u which does not scatter must be the solitary wave eitQ up to phase rotation and scaling.