{
  "abstract": "We study nonnegative entire spacelike graphs in Lorentz--Minkowski space satisfying $σ_k(A[u])=u^p$. For $2\\le k<n$ and $p\\ge k$, pointwise strict spacelikeness and closed $k$-admissibility yield universal bounds for the height and Lorentz factor. Their proof combines block coercivity in the full Gårding cone, a Lorentzian cutoff, and hyperbolic-cap comparison. For $2\\le k<n/2$ and $k\\le p\\le k(n+2)/(n-2k)$, every such solution vanishes, without symmetry, decay, finite-energy, curvature-pinching, or global Hessian assumptions. In the subcritical range we use a trace-free Newton tensor, a weighted divergence identity, and a finite descent. At the critical endpoint, the divergence identity retains an exact nonnegative defect and a positive quartic term. Direct estimates cover $2k<n\\le4k+2$. For $n\\ge4k+3$, we use compactness, concentration of the $k$-Hessian measure at the first crossing, a single-pole Pohozaev argument, core counting, a recursive defect estimate, and Souplet-type radius selection. A geometric corollary gives a rigidity result for complete spacelike immersions under the corresponding curvature equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25170",
  "author_total": 2,
  "authors": [
    {
      "name": "Shujun Shi"
    },
    {
      "name": "Yuzhou Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7g7bed6234x3x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25170",
  "fulltext_url": null,
  "id": "7g7bed6234x3x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25170",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214246181",
  "pdf_url": "https://arxiv.org/pdf/2609.25170",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7g7bed6234x3x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.25170",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25170"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Universal Spacelikeness Estimates and Liouville Rigidity for Lorentzian $σ_k$ Curvature Equations",
  "title_text": "Universal Spacelikeness Estimates and Liouville Rigidity for Lorentzian σ_k Curvature Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/7g7bed6234x3x",
  "venue": "arXiv",
  "versions": []
}