{
  "abstract": "In this paper, we give a negative answer to Wang's conjecture. For every $n\\geq 3$, there exist $\\varepsilon>0$ and $δ\\in (0,1)$ such that, for all $q$ and $λ$ satisfying \\[ \\frac{n}{n-2}-\\varepsilon<q\\le \\frac{n}{n-2}, \\qquad \\frac{1}{q-1}\\cdot δ<λ\\le \\frac{1}{q-1}, \\] there exists a bounded Euclidean domain \\(Ω\\subset\\mathbb{R}^n\\) with principal curvatures bigger than \\(1\\) for which the following nonlinear Robin problem admits a nonconstant positive solution: \\begin{align*} \\begin{cases} Δu=0, & \\text{in}\\ Ω,\\\\[2mm] \\dfrac{\\partial u}{\\partialν}+λu=u^q, & \\text{on}\\ \\partialΩ. \\end{cases} \\end{align*}",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13079",
  "author_total": 2,
  "authors": [
    {
      "name": "Ruiqi Jiang"
    },
    {
      "name": "Linlin Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ag3adm9s89bdz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13079",
  "fulltext_url": null,
  "id": "ag3adm9s89bdz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13079",
  "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|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212974623",
  "pdf_url": "https://arxiv.org/pdf/2609.13079",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ag3adm9s89bdz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.13079",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13079"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Counterexamples to Wang's Conjecture",
  "title_text": "Counterexamples to Wang's Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/ag3adm9s89bdz",
  "venue": "arXiv",
  "versions": []
}