{
  "abstract": "We study the focusing mass-critical inhomogeneous nonlinear Schrödinger equation $i\\partial_{t}u+Δu+|x|^{-b}|u|^{\\frac{4-2b}{d}}u=0$ in dimensions $d\\ge3$. For $\\frac12<b<\\min\\{2,d/2\\}$, we prove that every forward-global $H^1$ solution with mass equal to that of the ground state $Q$ either scatters forward or coincides with $e^{it}Q$, up to phase rotation and scaling. As a consequence, every solution with nonradial $H^1$ initial data at the ground-state mass must be global and scatter in both time directions. For $0<b\\le\\frac12$, analogous rigidity and scattering results hold under an additional finite-variance assumption. The key new ingredients in our proof are a nonradial incoming/outgoing decomposition and exterior frequency-decay estimates, which yield the kinetic-energy localization needed for a localized virial argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38285",
  "author_total": 1,
  "authors": [
    {
      "name": "Xuan Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3d2ezd7dhwstc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38285",
  "fulltext_url": null,
  "id": "3d2ezd7dhwstc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38285",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38285",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3d2ezd7dhwstc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38285",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38285"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Classification of threshold dynamics for the focusing mass-critical inhomogeneous NLS",
  "title_text": "Classification of threshold dynamics for the focusing mass-critical inhomogeneous NLS",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/3d2ezd7dhwstc",
  "venue": "arXiv",
  "versions": []
}