{
  "abstract": "We establish codimension-independent mass bounds for geometrically confined area-minimizing rectifiable currents. In Euclidean space, we combine the confined-volume doubling theorem of Colding--Minicozzi with a current-theoretic squashing argument. This gives an affirmative answer to Lin's interior mass-bound problem for every algebraic projection multiplicity $Q$: the interior mass is bounded by $C(n)Q$, without an a priori mass bound at a larger scale. This result yields a degree-one Bernstein-type rigidity result under sublinear confinement. For the hyperbolic application, we make the curvature modification of the fixed-scale argument needed in a thin tubular neighborhood of a totally geodesic copy of $\\mathbb{H}^n$. Combining this auxiliary estimate with a localized squashing estimate removes the doubly exponential local mass-growth condition from the boundary regularity results in [13].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01324",
  "author_total": 2,
  "authors": [
    {
      "name": "Xumin Jiang"
    },
    {
      "name": "Jiongduo Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ea1r2hd8f23m2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01324",
  "fulltext_url": null,
  "id": "ea1r2hd8f23m2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01324",
  "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": "W7206184902",
  "pdf_url": "https://arxiv.org/pdf/2609.01324",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ea1r2hd8f23m2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.01324",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01324"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Mass Bounds for Confined Area-Minimizing Minimal Surfaces",
  "title_text": "Mass Bounds for Confined Area-Minimizing Minimal Surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/ea1r2hd8f23m2",
  "venue": "arXiv",
  "versions": []
}