{
  "abstract": "In this paper, we establish symmetry results for solutions of the mean field equation \\[ \\fracα{2} Δu + e^u - 1 = 0 \\] on $ \\mathbb{S}^2 $ for $\\frac{1}{3}\\leq α\\leq 1$, under a geometric condition $(\\mathcal{H})$ introduced below. The proofs utilize the Sphere Covering Inequality and incorporate topological arguments on $ \\mathbb{S}^2 $. These results are further applied to demonstrate a rigidity property of the Hawking mass for stable constant mean curvature (CMC) spheres, addressing a question posed by Robert Bartnik in 2002. Our results unify and extend previous rigidity results obtained under symmetry or hemispherical balance assumptions, and apply beyond the nearly spherical setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.15448",
  "author_total": 2,
  "authors": [
    {
      "name": "Changfeng Gui"
    },
    {
      "name": "Amir Moradifam"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/03rg811ry8gkt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.15448",
  "fulltext_url": null,
  "id": "03rg811ry8gkt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.15448",
  "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"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7161538683",
  "pdf_url": "https://arxiv.org/pdf/2605.15448",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/03rg811ry8gkt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2605.15448",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.15448"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Symmetry and Rigidity Results for the Mean Field Equation and Hawking Mass on $\\mathbb{S}^2$",
  "title_text": "Symmetry and Rigidity Results for the Mean Field Equation and Hawking Mass on 𝕊^2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/03rg811ry8gkt",
  "venue": "arXiv",
  "versions": []
}