{
  "abstract": "This survey presents heat kernel regularization as a method for quantitative stability of Kantorovich potentials for the quadratic transport cost. We give a complete new heat kernel proof on Heisenberg groups equipped with the Carnot--Carathéodory distance. For source densities bounded above and away from zero on bounded John domains, we obtain $L^2$ stability with rate $W_1^{1/2}$ for arbitrary targets in a fixed compact set, including atomic measures. We also establish a new $L^2$ stability estimate on finite-dimensional RCD spaces, with the optimal dimension-independent exponent $1/2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39213",
  "author_total": 2,
  "authors": [
    {
      "name": "Bang-Xian Han"
    },
    {
      "name": "Zhuo-Nan Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dvtjag9q7wvqq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39213",
  "fulltext_url": null,
  "id": "dvtjag9q7wvqq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39213",
  "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.MG"
    ],
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      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W7215076832",
  "pdf_url": "https://arxiv.org/pdf/2609.39213",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dvtjag9q7wvqq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39213",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39213"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Stability of Kantorovich potentials via heat kernel regularization",
  "title_text": "Stability of Kantorovich potentials via heat kernel regularization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/dvtjag9q7wvqq",
  "venue": "arXiv",
  "versions": []
}