{
  "abstract": "We prove global well-posedness and scattering for the energy-critical defocusing nonlinear Schrödinger equation \\begin{equation*} \\begin{cases} i\\partial_t u + Δu = |u|^{\\frac{4}{d-2}} u, u(0) = u_0, \\end{cases} \\end{equation*} on hyperbolic space $\\mathbb{H}^d(d \\geq 4)$. We mainly utilize the concentration-compactness/rigidity method. We establish a linear profile decomposition on high-dimensional hyperbolic spaces and prove that the nonlinear profile on hyperbolic spaces can be approximated by the solutions of the energy-critical defocusing nonlinear Schrödinger equation on Euclidean spaces, then obtaining the global well-posedness and scattering of the energy-critical defocusing nonlinear Schrödinger equation on the high-dimensional hyperbolic space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37077",
  "author_total": 3,
  "authors": [
    {
      "name": "Shunqin Zhang"
    },
    {
      "name": "Jiqiang Zheng"
    },
    {
      "name": "Yunrui Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7hrxzxqtx34rf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37077",
  "fulltext_url": null,
  "id": "7hrxzxqtx34rf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37077",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7224128109",
  "pdf_url": "https://arxiv.org/pdf/2610.37077",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7hrxzxqtx34rf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37077",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37077"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global well-posedness and scattering of energy-critical defocusing nonlinear Schrödinger equation on high-dimensional hyperbolic spaces",
  "title_text": "Global well-posedness and scattering of energy-critical defocusing nonlinear Schrödinger equation on high-dimensional hyperbolic spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/7hrxzxqtx34rf",
  "venue": "arXiv",
  "versions": []
}