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

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arxiv 2310.12277 v2 pith:IF2S54ZH submitted 2023-10-15 math.AP

Bobby Wilson , Xueying Yu This is my paper · ORCID
classification math.AP
keywords spacedefocusingequationhyperbolicmass-criticalmathbbodingerschr
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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 $L^2 (\mathbb{H}^3)$.

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  1. Equivariant stability of vortices in Manton's Chern-Simons-Schr\"odinger system on the hyperbolic plane

    math.AP 2025-09 conditional novelty 6.0 of 10

    For each degree m≥1, sufficiently small equivariant perturbations of the m-vortex in Manton's self-dual Chern-Simons-Schrödinger model on H² yield a global solution with uniform Strichartz bounds.

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