{
  "abstract": "We show the existence of ultralimits of sequences of Hajlasz-Sobolev mappings $f_i:X_i\\to Y_i$ when $X_i$ converges to a limit space in the pointed measured Gromov (pmG) sense, partially extending recent results in [T. Ikonen and S. Wenger, (2026), arXiv:2603.05246]. We moreover demonstrate that the mappings pmG-converge to the ultralimit in a suitable sense, and obtain Arzela-Ascoli theorems in the context of pmG-convergence. As an application, we establish a version of Preiss's phenomenon for Hajlasz-Sobolev maps $f:(X,μ)\\to V$ into arbitrary Banach spaces. Besides extending it to maps into infinite dimensional targets, our result generalizes existing versions of Preiss's phenomenon [G. C. David, Geom. Funct. Anal., 25 (2015)], [N. Gigli, A. Mondino, and T. Rajala, J. Reine Angew. Math., 705 (2015)] by establishing it for pointed measured Gromov-Hausdorff tangents without a doubling assumption.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.13124",
  "author_total": 2,
  "authors": [
    {
      "name": "Milica Caković"
    },
    {
      "name": "Elefterios Soultanis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cqyc2zv0ga4xv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.13124",
  "fulltext_url": null,
  "id": "cqyc2zv0ga4xv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.13124",
  "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.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7203489318",
  "pdf_url": "https://arxiv.org/pdf/2608.13124",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cqyc2zv0ga4xv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2608.13124",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.13124"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Limits of mapping packages and tangents of Sobolev maps",
  "title_text": "Limits of mapping packages and tangents of Sobolev maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/cqyc2zv0ga4xv",
  "venue": "arXiv",
  "versions": []
}