{
  "abstract": "Let $(M^{n+1},g)$ be a compact Riemannian manifold with boundary. Under the assumptions $\\Ric_g\\geq ng$ and $\\II_g\\geq0$, Wang proposed a sharp strengthening of the Choi--Wang--Reilly estimate, asserting that the first nonzero Laplace eigenvalue of the boundary is at least $n$; see [J. Geom. Anal. 31 (2021)]. We disprove this assertion in every dimension $n+1\\geq3$. More precisely, we construct a sequence of metrics on the hemisphere $\\Sph^{n+1}_{+}$ converging in $C^\\infty$ to the round metric and satisfying \\[ \\Ric_g>n g,\\qquad \\II_g>0,\\qquad λ_1(\\partial\\Sph^{n+1}_{+},g|_{\\partial\\Sph^{n+1}_{+}})<n. \\] The construction starts from Zhu's infinitesimal conformal deformation, which lowers one branch of the first boundary eigenspace while preserving the normalized Ricci lower bound to first order. We add a multiple of the spherical height function.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.25391",
  "author_total": 2,
  "authors": [
    {
      "name": "Fagui Li"
    },
    {
      "name": "Yuhang Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/emdm8hbrtnndc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.25391",
  "fulltext_url": null,
  "id": "emdm8hbrtnndc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.25391",
  "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": "W7204435088",
  "pdf_url": "https://arxiv.org/pdf/2608.25391",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/emdm8hbrtnndc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.25391",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.25391"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Conformal Boundary Deformations under Ricci Lower Bounds: Eigenvalue Counterexamples",
  "title_text": "Conformal Boundary Deformations under Ricci Lower Bounds: Eigenvalue Counterexamples",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/emdm8hbrtnndc",
  "venue": "arXiv",
  "versions": []
}