{
  "abstract": "We introduce determinantal ellipticity, or det-ellipticity, a quantitative structural condition for fully nonlinear elliptic operators on compact Kähler manifolds that provides the link between the $L^\\infty$-estimates and algebraic/combinatorial properties of a large class of Hessian elliptic operators. On the analytic side, we introduce $\\mathcal D$-subsolutions extending the determinant sublevel condition of Sui--Sun. Using the auxiliary comparison method of Guo--Phong--Tong and pluripotential theory for complex Monge--Ampère equations, we obtain relative $L^\\infty$-estimates in big cohomology classes under a determinant-entropy bound for viscosity supersolutions and singular reference potentials. Det-ellipticity provides a systematic construction of such subsolutions. On the algebraic side, we study Gårding elliptic polynomial operators of degree $d$. We characterize the determinant increment bound with exponent $d/n$ by positivity of the determinantal capacity of the top homogeneous part. This is equivalent to balanced-point conditions for the Newton polytopes of rank-one scalarizations and to slope semistability of an associated subspace polymatroid. Together with the analytic hypotheses, these criteria yield relative $L^\\infty$ estimates for the corresponding fully nonlinear equations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24078",
  "author_total": 3,
  "authors": [
    {
      "name": "Hao Fang"
    },
    {
      "name": "Biao Ma"
    },
    {
      "name": "Jinyang Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e5mgzpprvy6c1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24078",
  "fulltext_url": null,
  "id": "e5mgzpprvy6c1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24078",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7214050937",
  "pdf_url": "https://arxiv.org/pdf/2609.24078",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e5mgzpprvy6c1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24078",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24078"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Determinantal capacity and $L^\\infty$-Estimates",
  "title_text": "Determinantal capacity and L^∞-Estimates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/e5mgzpprvy6c1",
  "venue": "arXiv",
  "versions": []
}