{
  "abstract": "Let $Γ<SO(4)$ be a nontrivial finite group acting freely on $S^3$, and let $M=S^3/Γ$. We prove that every smooth conformal class $C$ on $M$ satisfies \\[ Y(M,C)\\le |Γ|^{-2/3}Y(S^3), \\] with equality for the quotient-round conformal class. Consequently, \\[ σ(M)=|Γ|^{-2/3}Y(S^3). \\] Our approach uses four-dimensional Poincaré--Einstein fillings of the ball. We first establish compactness for fillings whose conformal infinities range over a compact family of positive-scalar-curvature metrics. Since compactness alone does not guarantee continuation through degenerate Einstein metrics, we use equivariant Fredholm parity to obtain a filling with the prescribed boundary conformal class and group action. A common interior fixed point then makes the Li--Qing--Shi boundary test function invariant, and its descent to $M$ gives the sharp covering factor.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18793",
  "author_total": 1,
  "authors": [
    {
      "name": "Jakob Loren"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/drxsmf5nk73cp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18793",
  "fulltext_url": null,
  "id": "drxsmf5nk73cp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18793",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7221758107",
  "pdf_url": "https://arxiv.org/pdf/2610.18793",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/drxsmf5nk73cp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18793",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18793"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Sharp Yamabe Bounds for Spherical Three-Space Forms via Four-Dimensional Poincaré--Einstein Compactness",
  "title_text": "Sharp Yamabe Bounds for Spherical Three-Space Forms via Four-Dimensional Poincaré--Einstein Compactness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/drxsmf5nk73cp",
  "venue": "arXiv",
  "versions": []
}