{
  "abstract": "Let $(M,g)$ be a connected, compact, $n$-dimensional Riemannian manifold with $\\operatorname{Ric}(M,g)\\geq-(n-1)κg$. We introduce a weighted combinatorial Laplacian on $\\varepsilon$-discretizations of $M$ and prove a spectral comparison theorem between the weighted graph Laplacian and the Laplace-Beltrami operator. More precisely, the eigenvalues of the two operators are uniformly comparable with constants depending only on $n,κ,\\varepsilon$, independently of the injectivity radius. As an application, we prove spectral stability under measured Gromov-Hausdorff convergence. We also recover the Schoen-Wolpert-Yau inequality using the weighted discretization on families of pinching genus-$2$ hyperbolic surfaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.02405",
  "author_total": 1,
  "authors": [
    {
      "name": "Aditya Tiwari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8a1h06nt7x309.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.02405",
  "fulltext_url": null,
  "id": "8a1h06nt7x309",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.02405",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7172427754",
  "pdf_url": "https://arxiv.org/pdf/2608.02405",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8a1h06nt7x309.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2608.02405",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.02405"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Weighted Discretization of Riemannian Manifolds with Lower Ricci Bounds",
  "title_text": "A Weighted Discretization of Riemannian Manifolds with Lower Ricci Bounds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/8a1h06nt7x309",
  "venue": "arXiv",
  "versions": []
}