{
  "abstract": "We study the behaviour of the conjugate radius under the Ricci flow on complete noncompact manifolds. We show that if $(M^n,g(t))_{t\\in[0,T]}$ is a complete Ricci flow with nonnegative scalar curvature at $t=0$, the initial metric is parabolic and not Ricci-flat, and the Einstein tensor $\\mathrm{Ric}-\\tfrac12 Rg$ is bounded above, then parabolicity is preserved along the flow and the conjugate radius of $g(t)$ is finite for every $t\\in(0,T]$. As an application, we prove that a complete noncompact gradient shrinking Ricci soliton whose volume growth is subquadratic, in the sense that $\\liminf_{r\\to\\infty}\\Vol(B(p,r))/r^2=0$, has finite conjugate radius.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03823",
  "author_total": 1,
  "authors": [
    {
      "name": "Chandan Kumar Mondal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8nb5asz61a509.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03823",
  "fulltext_url": null,
  "id": "8nb5asz61a509",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03823",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03823",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8nb5asz61a509.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.03823",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03823"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Conjugate radius and parabolicity along the Ricci flow",
  "title_text": "Conjugate radius and parabolicity along the Ricci flow",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:38Z",
  "url": "https://research.draconitic.com/paper/8nb5asz61a509",
  "venue": "arXiv",
  "versions": []
}