{
  "abstract": "We study generalized Young measures generated by $\\mathscr{A}$-free measures, $\\mathscr{A}$ a constant-rank operator, in a compactification of the value space adapted to an energy. Given an $\\mathscr{A}$-quasiconvex integrand $G$ of linear growth with coercive recession function $G^\\infty$, the unit sphere at infinity is replaced by the indicatrix $\\mathbb{S}_G=\\{G^\\infty=1\\}$, which need be neither convex nor symmetric. The two compactifications are equivalent, but in the adapted one the equality cases of the Jensen inequalities characterizing $\\mathscr{A}$-free Young measures become statements of convex geometry about $\\mathbb{S}_G$. We prove the characterization in this setting, with a new streamlined proof of the inhomogenization step based on a dyadic martingale argument. We then show that if $\\mathscr{A}$-free measures $μ_j\\overset{*}{\\rightharpoonup}μ$ and their $G$-energies converge, then at $|μ^s|$-almost every point the concentration-angle measure is supported on the smallest exposed face of $\\overline{\\mathrm{co}}(\\mathbb{S}_G)$ containing the $G$-polar of $μ^s$; in particular, it never charges the set where $G^\\infty$ differs from its convex envelope, which, by the automatic convexity of Kirchheim and Kristensen, does not meet the wave cone. The concentration on the singular part of $μ$ is elementary for every such sequence if and only if each point of the wave cone on $\\mathbb{S}_G$ is an extreme point of $\\overline{\\mathrm{co}}(\\mathbb{S}_G)$, as for the Euclidean norm underlying Reshetnyak's continuity theorem; on flat faces of $\\mathbb{S}_G$, rigidity degrades from a point to a face. Finally, we prove a transfer principle for the convergence of energies of $\\mathrm{BV}$ maps under Dirichlet boundary conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22560",
  "author_total": 1,
  "authors": [
    {
      "name": "Sergio Scalabrino"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1jhdr4at6grey.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22560",
  "fulltext_url": null,
  "id": "1jhdr4at6grey",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22560",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7222954223",
  "pdf_url": "https://arxiv.org/pdf/2610.22560",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1jhdr4at6grey.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.22560",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22560"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Geometric rigidity principles for $\\mathscr{A}$-free Young measures",
  "title_text": "Geometric rigidity principles for 𝒜-free Young measures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/1jhdr4at6grey",
  "venue": "arXiv",
  "versions": []
}