{
  "abstract": "Given a bounded open set $V\\subset \\mathbb{R}^2$, we consider the problem of slicing this set by a family of curves, whose average length is as small as possible. The first sections of the paper prove the existence of an optimal slicing and establish a connection with the problem of eradicating an invasive biological species from an island, considered in \\cite{BMS}. Namely, an optimal slicing can be obtained as a limit of minimum time eradication strategies. The second part of the paper derives various necessary conditions for optimality, describing the behavior of an optimal slicing strategy in the interior of $V$ and near the boundary $\\partial V$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36149",
  "author_total": 3,
  "authors": [
    {
      "name": "Alberto Bressan"
    },
    {
      "name": "Maria Teresa Chiri"
    },
    {
      "name": "Elsa M. Marchini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4rsv8da7g5vpk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36149",
  "fulltext_url": null,
  "id": "4rsv8da7g5vpk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36149",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214990927",
  "pdf_url": "https://arxiv.org/pdf/2609.36149",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4rsv8da7g5vpk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36149",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36149"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Optimal Slicing Problems",
  "title_text": "Optimal Slicing Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/4rsv8da7g5vpk",
  "venue": "arXiv",
  "versions": []
}