{
  "abstract": "We study asymptotic properties of critical points of the two-dimensional vectorial Allen-Cahn energy with finitely many non-degenerate wells, subject to a homogeneous Neumann boundary condition. For any sequence with uniformly bounded energy, we prove that the limiting full and potential measures are supported on a closed countably 1-rectifiable set up to the boundary and satisfy the discrepancy relations. The potential measure defines a free-boundary stationary rectifiable varifold. Boundary mass may occur: weights are constant on regular boundary arcs, finite-type junctions obey projected balance, and the sole non-boundary branch meets the boundary orthogonally. This provides a Neumann-boundary extension of Bethuel's planar interior theory. The key idea is to read the boundary geometry from the limiting stress-energy tensor, which identifies the potential-energy measure as the stationary interfacial measure even in the presence of boundary concentration.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00739",
  "author_total": 4,
  "authors": [
    {
      "name": "Zhiyuan Dai"
    },
    {
      "name": "Haotong Fu"
    },
    {
      "name": "Huaijie Wang"
    },
    {
      "name": "Wei Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1e5gvp54sajnk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00739",
  "fulltext_url": null,
  "id": "1e5gvp54sajnk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00739",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7206184176",
  "pdf_url": "https://arxiv.org/pdf/2609.00739",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1e5gvp54sajnk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00739",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00739"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Boundary asymptotics for two-dimensional vectorial Allen-Cahn systems",
  "title_text": "Boundary asymptotics for two-dimensional vectorial Allen-Cahn systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/1e5gvp54sajnk",
  "venue": "arXiv",
  "versions": []
}