We consider the focusing cubic nonlinear Schrödinger equation with inverse-square potential in three space dimensions. We identify a sharp threshold between scattering and blowup, establishing a result analogous to that of Duyckaerts, Holmer, and Roudenko for the standard focusing cubic NLS [7, 11]. We also prove failure of uniform space-time bounds at the
"The focusing cubic NLS with inverse-square potential in three space dimensions." Differential Integral Equations 30 (3/4) 161 - 206, March/April 2017.