{
  "abstract": "In this paper, let $u\\in C^4(B_{10})$ with $D^2u\\geq -KI$ define a $2$-admissible graph $M=\\{(x,u(x)):x\\in B_{10}\\}\\subset\\R^{n+1}$ satisfying \\[ σ_2(κ[u])=f(x). \\] We prove an interior curvature estimate depending on the Lipschitz norm of the right-hand sides. The proof combines a shifted Jacobi inequality for \\(b=\\log(H+J_0)\\), a parallel hypersurface transformation that makes the Newton tensor uniformly elliptic and local boundedness estimate then reduces the pointwise bound to a weighted $L^1$ estimate, which is completed using the Jacobi energy inequality and integration by parts.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03958",
  "author_total": 1,
  "authors": [
    {
      "name": "Lichun Liang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2b0jkg4kz8dkj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03958",
  "fulltext_url": null,
  "id": "2b0jkg4kz8dkj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03958",
  "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": "W7208736225",
  "pdf_url": "https://arxiv.org/pdf/2609.03958",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2b0jkg4kz8dkj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03958",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03958"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Interior Curvature Estimates of Semi-convex Solutions for the scalar curvature equation with Lipschitz Right-Hand Sides",
  "title_text": "Interior Curvature Estimates of Semi-convex Solutions for the scalar curvature equation with Lipschitz Right-Hand Sides",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/2b0jkg4kz8dkj",
  "venue": "arXiv",
  "versions": []
}