{
  "abstract": "We prove that the capillary $L_p$ dual Minkowski problem in $\\mathbb{R}^{n+1}$, $n\\geq3$, admits a unique positive smooth strictly convex solution for any prescribed positive smooth function $f$ when $p>q$ and the contact angle satisfies $θ\\in(0,π/2)$. Earlier results for $p>q$ either required the additional condition $q\\leq1$ or were restricted to $n=2$. We reduce the problem to a Monge--Ampère type equation with a Robin boundary condition on a spherical cap. By constructing a new auxiliary function for the global $C^2$ estimate, we overcome these limitations and completely resolve the case of $p>q$ in higher dimensions, i.e., prove existence and uniqueness throughout the case of $p>q$, without any further restriction on $p$ or $q$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07158",
  "author_total": 1,
  "authors": [
    {
      "name": "Ya Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4sq5ke3cwjgn5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07158",
  "fulltext_url": null,
  "id": "4sq5ke3cwjgn5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07158",
  "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",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7212051130",
  "pdf_url": "https://arxiv.org/pdf/2609.07158",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4sq5ke3cwjgn5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2609.07158",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07158"
    }
  ],
  "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 Minkowski problem for $p>q$ in higher dimensions",
  "title_text": "The capillary L_p dual Minkowski problem for p>q in higher dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/4sq5ke3cwjgn5",
  "venue": "arXiv",
  "versions": []
}