{
  "abstract": "We study an exterior Bernoulli-type free boundary problem associated with the Riemannian $p$-Laplacian on a compact Riemannian manifold. Following the shape-optimization strategy of Ly and Seck, we formulate the corresponding volume-constrained shape optimization problem, derive its first shape derivative, obtain the overdetermined Bernoulli condition through a Lagrange multiplier, and establish a conditional monotonicity result under a Riemannian contraction hypothesis. The final successive-approximation argument will require additional geometric and boundary-flux stability assumptions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00571",
  "author_total": 2,
  "authors": [
    {
      "name": "Ababacar Sadikhe Djite"
    },
    {
      "name": "Diaraf Seck"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4txexbhmtejdx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00571",
  "fulltext_url": null,
  "id": "4txexbhmtejdx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00571",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7206166570",
  "pdf_url": "https://arxiv.org/pdf/2609.00571",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4txexbhmtejdx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.00571",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00571"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Shape Optimization and Bernoulli Free Boundary Problems for the Riemannian $p$-Laplacian",
  "title_text": "Shape Optimization and Bernoulli Free Boundary Problems for the Riemannian p-Laplacian",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/4txexbhmtejdx",
  "venue": "arXiv",
  "versions": []
}