{
  "abstract": "In this paper, we establish several sharp comparsion results for noncompact 3-manifolds with nonnegative scalar curvature and with a compact, connected boundary under a boundary mean curvature condition. Then we apply these gradient estimates to establish a Cohn-Vossen type bound for the average of the scalar curvature. This generalizes the work of Colding-Minicozzi \\cite{Cold4} and Oronzio \\cite{Oro2}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.11331",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiannan Chen"
    },
    {
      "name": "Haiping Fu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/65bqezetnx6jk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.11331",
  "fulltext_url": null,
  "id": "65bqezetnx6jk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.11331",
  "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.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.11331",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/65bqezetnx6jk.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:34Z",
      "native_id": "2611.11331",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.11331"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Harmonic functions and comparsion geometry for noncompact 3-manifolds with nonnegative scalar curvature",
  "title_text": "Harmonic functions and comparsion geometry for noncompact 3-manifolds with nonnegative scalar curvature",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:34Z",
  "url": "https://research.draconitic.com/paper/65bqezetnx6jk",
  "venue": "arXiv",
  "versions": []
}