{
  "abstract": "For a convex surface tension $φ$ and the wall-energy density $σ(n)=-λ\\,φ(-n)$, we prove sharp capillary inequalities outside arbitrary convex planar obstacles for $-1<λ\\leq0$ and every finite-perimeter competitor of finite positive volume, including non-even and crystalline tensions. Equality holds precisely for translated dilates of Wulff caps in minimum-volume directions, with the entire truncating facet resting on a flat supporting face. A uniform quantitative estimate controls component concentration, shape up to translation, and directional cap-volume excess. The proof combines exact filling, planar completion, and quantitative Wulff stability. For the transport $DΦ$, $Φ=φ^2/2$, the zero-adhesion boundary-image estimate characterizes centered ellipsoids among even anisotropies with $Φ\\in C^3$ away from the origin and positive definite Hessian. Two-point slab tests with arbitrary boundary data suffice: their projection balances yield a cubic identity forcing $Φ$ to be quadratic. Facets and smooth perturbations provide counterexamples to the transported estimate, including failures at prescribed adhesion levels in $(-1,1)$. Strict finite deficits persist under Hausdorff perturbations of the Wulff body. The classification concerns an unrestricted boundary-data property, stronger than the image estimate needed only for traces of auxiliary Neumann solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37440",
  "author_total": 3,
  "authors": [
    {
      "name": "Lisbeth Carrero"
    },
    {
      "name": "Alexander Quaas"
    },
    {
      "name": "Andres Zuniga"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8my5kbffjsz94.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37440",
  "fulltext_url": null,
  "id": "8my5kbffjsz94",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37440",
  "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": "W7224110611",
  "pdf_url": "https://arxiv.org/pdf/2610.37440",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8my5kbffjsz94.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37440",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37440"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp Planar Anisotropic Capillarity Outside Convex Obstacles and Two-Point Rigidity of Transported Boundary Images",
  "title_text": "Sharp Planar Anisotropic Capillarity Outside Convex Obstacles and Two-Point Rigidity of Transported Boundary Images",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/8my5kbffjsz94",
  "venue": "arXiv",
  "versions": []
}