{
  "abstract": "We study three variational problems for Einstein metrics with conical limits. For every $k\\ge5$, the complete Ricci-flat Böhm metric on $\\mathbb{R}^{k+1}\\times S^k$ has holonomy $SO(2k+1)$ and a homogeneous coercive estimate on all symmetric two-tensors. It attracts sufficiently small smooth $L^2\\cap C_b^{2,\\eta}$ perturbations under the fixed-background Ricci–DeTurck flow, with convergence in $L^2$ and every uniform $C^j$ norm. Uniformly small ancient perturbations with bounded $L^2$ norm are stationary. For $p,q\\ge2$ and $p+q\\le8$, we construct distinct normalized Einstein volumes on $S^{p+q+1}$, on $S^{p+1}\\times Q$ for every closed connected positive Einstein $q$-manifold $Q$, and on the specified identity doubles of disk bundles with vanishing O'Neill tensor. Their full Einstein moduli spaces have infinitely many connected components. The volumes approach the sine-cone value from above; specified subsequences have geometric asymptotics. On a marked conical end of rate greater than $(n-2)/2$, with absolutely integrable scalar curvature, a large-scale upper bound for Perelman's $\\mu$-functional has coefficient $\\lambda_{\\mathrm{nc}}-\\mathfrak m_C$. No spin or scalar-curvature sign is assumed in this comparison. A parallel spinor compatible with the end induced in the universal cover gives mass–energy rigidity and characterizes equality in the global cone entropy bound by Ricci-flatness. Equality also makes the end homomorphism surjective with finite image and extends the compatible cone spinors. An ancient Ricci flow with one such slice is stationary when its finite backward Nash entropy is at least the cone value.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Anass Nifa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bmz46yzzaej0b.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.22914134",
  "fulltext_url": null,
  "id": "bmz46yzzaej0b",
  "issns": [],
  "landing_url": "https://hal.science/hal-05769958v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-dg"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05769958/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bmz46yzzaej0b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:43Z",
      "native_id": "hal-05769958",
      "source": "hal",
      "url": "https://hal.science/hal-05769958v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-dg",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Einstein metrics at conical limits: stability, disconnected moduli, and entropy rigidity",
  "title_text": "Einstein metrics at conical limits: stability, disconnected moduli, and entropy rigidity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:43Z",
  "url": "https://research.draconitic.com/paper/bmz46yzzaej0b",
  "venue": "HAL",
  "versions": []
}