{
  "abstract": "We characterize Gromov-compactifiability of Wasserstein spaces over Polish metric spaces for $1\\leq p\\leq\\infty$. The space $\\mathcal{P}_1(X)$ is Gromov-compactifiable if and only if $X$ is bounded and Gromov-compactifiable, whereas $\\mathcal{P}_p(X)$ is Gromov-compactifiable for every $1<p<\\infty$. At the other endpoint, $\\mathcal{P}_\\infty(X)$ is Gromov-compactifiable if and only if $X$ is. For $p=1$, the sufficiency argument combines an averaged triangle defect with tightness. For $1<p<\\infty$, the main tool is the uniform convexity of $L^p$. The $p=\\infty$ proof uses the finite-set criterion and a mass redistribution construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12355",
  "author_total": 2,
  "authors": [
    {
      "name": "Huajian Jiang"
    },
    {
      "name": "Zhi-Xiang Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e7fqab3nt30qt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12355",
  "fulltext_url": null,
  "id": "e7fqab3nt30qt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12355",
  "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.MG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212610460",
  "pdf_url": "https://arxiv.org/pdf/2609.12355",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e7fqab3nt30qt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12355",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12355"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Gromov-compactifiability of Wasserstein spaces",
  "title_text": "Gromov-compactifiability of Wasserstein spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/e7fqab3nt30qt",
  "venue": "arXiv",
  "versions": []
}