Global well-posedness and scattering for the focusing nonlinear Schrödinger equation in the nonradial case

The energy-critical, focusing nonlinear Schrödinger equation in the nonradial case reads as follows: [formula]. Under a suitable assumption on the maximal strong solution, using a compactness argument and a virial identity, we establish the global well-posedness and scattering in the nonradial case, which gives a positive answer to one open problem proposed by Kenig and Merle [Invent. Math. 166 (2006), 645-675].