{
  "abstract": "This paper investigates the $L_p$-dual mixed Euclidean-Gauss Minkowski problem associated with the $L_p$-dual mixed Euclidean-Gaussian curvature measure. The solvability of this problem is equivalent to that of a class of Monge-Ampère type equations on the unit sphere. Under smooth assumptions, We establish the existence of solutions for $p<1$, $q<0$, and $q<p$ and uniqueness of solutions for $p\\geq q$ to the aforementioned Monge-Ampère type equations, respectively. Furthermore, we obtain a complete solution concerning the existence part of this problem when $p<1$ and $q<0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23588",
  "author_total": 4,
  "authors": [
    {
      "name": "Na Fu"
    },
    {
      "name": "Jian-Ping Sun"
    },
    {
      "name": "Bin Chen"
    },
    {
      "name": "Ya-Hong Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f0ynrsr067fwy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23588",
  "fulltext_url": null,
  "id": "f0ynrsr067fwy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23588",
  "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": "W7214036453",
  "pdf_url": "https://arxiv.org/pdf/2609.23588",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f0ynrsr067fwy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23588",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23588"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The solvability of the $L_p$-dual mixed Euclidean-Gauss Minkowski problem",
  "title_text": "The solvability of the L_p-dual mixed Euclidean-Gauss Minkowski problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/f0ynrsr067fwy",
  "venue": "arXiv",
  "versions": []
}