Characterization of minimal-mass blowup solutions to the focusing mass-critical NLS Killip, Rowan Li, Dong Visan, Monica Zhang, Xiaoyi Let 𝑑 ≥4 and let u be a global solution to the focusing mass-critical nonlinear Schrödinger equation 𝑖⁢𝑢𝑡 +Δ⁢𝑢 =−|𝑢|4𝑑 ⁢𝑢 with spherically symmetric 𝐻1𝑥 initial data and mass equal to that of the ground state Q. We prove that if u does not scatter, then, up to phase rotation and scaling, u is the solitary wave 𝑒𝑖⁢𝑡⁢𝑄. Combining this result with that of Merle [Duke Math. J., 69 (1993), pp. 427–453], we obtain that in dimensions 𝑑 ≥4, the only spherically symmetric minimal-mass nonscattering solutions are, up to phase rotation and scaling, the pseudoconformal ground state and the ground state solitary wave. Society for Industrial & Applied Mathematics 2009 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22078 Killip R, Li D, Vişan M, Zhang X. Characterization of minimal-mass blowup solutions to the focusing mass-critical NLS. <i>SIAM Journal on Mathematical Analysis</i>. 2009;41(1):219-236. doi:<a href="https://doi.org/10.1137/080720358">10.1137/080720358</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1137/080720358 info:eu-repo/semantics/altIdentifier/issn/0036-1410 info:eu-repo/semantics/altIdentifier/e-issn/1095-7154 info:eu-repo/semantics/altIdentifier/arxiv/0804.1124 info:eu-repo/semantics/openAccess