{
  "abstract": "A vanishing sequence $V_n$ of divergence-free matrix fields is one that is bounded in $L^1$ and is carried by open sets $A_n$ of vanishing volume. Recently established, Bouchitté's vanishing mass conjecture says that the directions such a sequence can carry are rigidly constrained: their limiting distribution must be a superposition of microstructures whose barycenters are singular matrices. We prove the converse in the non-symmetric setting: every such superposition is attained by a vanishing sequence. In fact, we are able to construct divergence-free fields $V_n$ $supported$ on $A_n$, whose relative boundary is a smooth compact manifold.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24767",
  "author_total": 3,
  "authors": [
    {
      "name": "Adolfo Arroyo-Rabasa"
    },
    {
      "name": "Francesco Nobili"
    },
    {
      "name": "Ivan Yuri Violo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/52rd17455hxxq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24767",
  "fulltext_url": null,
  "id": "52rd17455hxxq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24767",
  "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"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214052049",
  "pdf_url": "https://arxiv.org/pdf/2609.24767",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/52rd17455hxxq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24767",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24767"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Divergence-free concentrations come from vanishing sequences",
  "title_text": "Divergence-free concentrations come from vanishing sequences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/52rd17455hxxq",
  "venue": "arXiv",
  "versions": []
}