{
  "abstract": "This paper is concerned with a capillary $L_p$ Christoffel--Minkowski-type problem involving the prescription of a class of $L_p$ geometric measures formed by the $k$-th capillary area measure and the $q$-th dual curvature measure. By establishing a gradient estimate, we prove the existence of an even, smooth, strictly convex solution in the parameter range $1<p<q\\leq k+1$, where $1\\leq k\\leq n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37258",
  "author_total": 2,
  "authors": [
    {
      "name": "Guanghan Li"
    },
    {
      "name": "Mengliang Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dv40kvmh2xmv1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37258",
  "fulltext_url": null,
  "id": "dv40kvmh2xmv1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37258",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7214961566",
  "pdf_url": "https://arxiv.org/pdf/2609.37258",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dv40kvmh2xmv1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37258",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37258"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The capillary $L_{p}$ dual Christoffel-Minkowski problem for $1<p<q\\leq k+1$ with $1\\leq k\\leq n$",
  "title_text": "The capillary L_p dual Christoffel-Minkowski problem for 1<p<q≤ k+1 with 1≤ k≤ n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/dv40kvmh2xmv1",
  "venue": "arXiv",
  "versions": []
}