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In this paper, we prove that the initial value problem for the mass-criticaldefocusing nonlinear Schr\"odinger equation on the three-dimensional hyperbolicspace $\mathbb{H}^3$ is globally well-posed and scatters for data with radialsymmetry in the critical space $L^2 (\mathbb{H}^3)$.

Global well-posedness and scattering for the defocusing mass-critical Schr\"odinger equation in the three-dimensional hyperbolic space