The focusing cubic NLS on exterior domains in three dimensions Killip, Rowan Visan, Monica Zhang, Xiaoyi 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 Press 2016 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22052 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1093/amrx/abv012 info:eu-repo/semantics/altIdentifier/issn/1687-1200 info:eu-repo/semantics/altIdentifier/e-issn/1687-1197 info:eu-repo/semantics/altIdentifier/arxiv/1501.05062 info:eu-repo/semantics/openAccess