{
  "abstract": "Let $(X,ω)$ be a compact Gauduchon manifold and let $E$ be a holomorphic vector bundle on $X$. We establish equivalent conditions for the existence of a Hermitian metric on $E$ with nonpositive mean curvature. For a non-uniruled compact Kähler manifold $X$ satisfying $μ_{ω_0,\\max}(T_X)=0$ for some Gauduchon metric $ω_0$, we show that the corresponding maximal destabilizing subsheaf of $T_X$ splits off holomorphically and is polystable of slope zero with respect to every Gauduchon metric. Its complement, if nonzero, is HN-negative with respect to every such metric. In particular, a compact Kähler manifold is not uniruled if and only if , for every Gauduchon metric $ω$, its tangent bundle admits a Hermitian metric with nonpositive $ω$-mean curvature. We also obtain an uniruledness criterion that includes the case where the maximal slope of $T_X$ is zero, and a Mumford-type characterization of rational connectedness. Under HN-nonnegativity of $T_X$ for one Gauduchon metric, rational connectedness, the vanishing of all holomorphic covariant tensors, and the condition $κ^+(X)=-\\infty$ are equivalent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29268",
  "author_total": 2,
  "authors": [
    {
      "name": "Chuanjing Zhang"
    },
    {
      "name": "Xi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5e6wjg26bfzcc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29268",
  "fulltext_url": null,
  "id": "5e6wjg26bfzcc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29268",
  "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.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7223229750",
  "pdf_url": "https://arxiv.org/pdf/2610.29268",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5e6wjg26bfzcc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29268",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29268"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Mean curvature nonpositivity and rational connectedness",
  "title_text": "Mean curvature nonpositivity and rational connectedness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/5e6wjg26bfzcc",
  "venue": "arXiv",
  "versions": []
}