{
  "abstract": "We extend reflection coupling for uniform-in-time propagation of chaos from Euclidean space to complete Riemannian manifolds. Intrinsic reflection along minimizing geodesics replaces the Euclidean difference process, and the associated endpoint-index term quantifies the competition between curvature, confinement, and interaction. Under an endpoint-index bound and a radial Laplacian bound, we establish global well-posedness, uniform moment estimates, and uniform-in-time propagation of chaos with rate $N^{-1/2}$ in a modified Wasserstein distance. We further obtain exponential contraction of the nonlinear McKean--Vlasov semigroup, uniqueness of its invariant probability measure among probability measures with finite second moment, and exponential convergence to equilibrium. Although a Ricci lower bound is an important special case, our framework also includes a curvature-spike class with $\\inf_M\\operatorname{Ric}=-\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12948",
  "author_total": 4,
  "authors": [
    {
      "name": "Myeongju Chae"
    },
    {
      "name": "Gunhee Cho"
    },
    {
      "name": "Hyun Chul Jang"
    },
    {
      "name": "Guang Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9bvk9vb0kgfqa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12948",
  "fulltext_url": null,
  "id": "9bvk9vb0kgfqa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12948",
  "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.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7213184597",
  "pdf_url": "https://arxiv.org/pdf/2609.12948",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9bvk9vb0kgfqa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.12948",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12948"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Propagation of Chaos on Riemannian Manifolds",
  "title_text": "Propagation of Chaos on Riemannian Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/9bvk9vb0kgfqa",
  "venue": "arXiv",
  "versions": []
}