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

Abstract

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