article published yes Rowan Killip author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca Xiaoyi Zhang author We consider the focusing cubic nonlinear Schrödinger equation (NLS) in the exterior Ω of a smooth, compact, strictly convex obstacle in three dimensions. We prove that the threshold for global existence and scattering is the same as for the problem posed on Euclidean space. Specifically, we prove that if E(u0)M(u0)<E(Q)M(Q) and ||u0||2||u0||2<\|\nabla Q||2||Q||2, the corresponding solution to the initial value problem with Dirichlet boundary conditions exists globally and scatters to linear evolutions asymptotically in the future and in the past. Here, Q(x) denotes the ground state for the focusing cubic NLS in ℝ3. Oxford University Press2016 eng 1687-1200 1687-1197 1501.0506210.1093/amrx/abv012 20161146-180 yes Killip R, Vişan M, Zhang X. The focusing cubic NLS on exterior domains in three dimensions. <i>Applied Mathematics Research eXpress</i>. 2016;2016(1):146-180. doi:<a href="https://doi.org/10.1093/amrx/abv012">10.1093/amrx/abv012</a> R. Killip, M. Vişan, X. Zhang, Applied Mathematics Research EXpress 2016 (2016) 146–180. Killip R, Vişan M, Zhang X. 2016. The focusing cubic NLS on exterior domains in three dimensions. Applied Mathematics Research eXpress. 2016(1), 146–180. R. Killip, M. Vişan, and X. Zhang, “The focusing cubic NLS on exterior domains in three dimensions,” <i>Applied Mathematics Research eXpress</i>, vol. 2016, no. 1. Oxford University Press, pp. 146–180, 2016. Killip, R., Vişan, M., &#38; Zhang, X. (2016). The focusing cubic NLS on exterior domains in three dimensions. <i>Applied Mathematics Research EXpress</i>. Oxford University Press. <a href="https://doi.org/10.1093/amrx/abv012">https://doi.org/10.1093/amrx/abv012</a> Killip, Rowan, et al. “The Focusing Cubic NLS on Exterior Domains in Three Dimensions.” <i>Applied Mathematics Research EXpress</i>, vol. 2016, no. 1, Oxford University Press, 2016, pp. 146–80, doi:<a href="https://doi.org/10.1093/amrx/abv012">10.1093/amrx/abv012</a>. Killip, Rowan, Monica Vişan, and Xiaoyi Zhang. “The Focusing Cubic NLS on Exterior Domains in Three Dimensions.” <i>Applied Mathematics Research EXpress</i>. Oxford University Press, 2016. <a href="https://doi.org/10.1093/amrx/abv012">https://doi.org/10.1093/amrx/abv012</a>. 220522026-06-19T07:54:24Z2026-06-25T08:30:19Z