{
  "abstract": "We establish a quantitative criterion for local Lipschitz regularity of Sobolev maps in the sense of Korevaar and Schoen from finite-dimensional \\(\\RCD(K,N)\\) spaces into complete \\(\\CAT(0)\\) spaces, without assuming harmonicity. We quantify the failure of local energy minimality by the harmonic replacement potential, a dyadic sum of the square roots of normalized energy gaps between a map and its harmonic replacements. We prove that this potential, together with an averaged energy term, controls the minimal weak upper gradient pointwise, with constants depending only on the curvature-dimension bounds and the scale. In particular, local boundedness of the replacement potential implies that the map admits a locally Lipschitz representative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39644",
  "author_total": 2,
  "authors": [
    {
      "name": "Bang-Xian Han"
    },
    {
      "name": "Zeyu Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bfsf4xmz5grvd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39644",
  "fulltext_url": null,
  "id": "bfsf4xmz5grvd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39644",
  "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.DG"
    ],
    [
      "arxiv",
      "math.MG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39644",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bfsf4xmz5grvd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39644",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39644"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Lipschitz regularity of Sobolev maps from $\\mathrm{RCD}(K,N)$ spaces to $\\mathrm{CAT}(0)$ spaces",
  "title_text": "Lipschitz regularity of Sobolev maps from RCD(K,N) spaces to CAT(0) spaces",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/bfsf4xmz5grvd",
  "venue": "arXiv",
  "versions": []
}