Global well-posedness and scattering for the defocusing mass-critical Schrödinger equation in the three-dimensional hyperbolic space

Abstract

In this paper, we prove that the initial value problem for the mass-critical defocusing nonlinear Schrödinger 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 $L^2({\mathbb{H}}^3)$.

arXiv admin note: substantial text overlap with arXiv:1008.1237 by other authors