{
  "abstract": "We study the sublevel sets of the Willmore energy on the space of smoothly immersed 2 $ 2 $ 2 -spheres in Euclidean 3 $ 3 $ 3 -space. We show that the subset of immersions with energy at most 12 π $ 12\\pi $ 12 pi consists of four regular homotopy classes. Moreover, we show that, in certain regular homotopy classes, all singularities of the Willmore flow are avoidable – that is, the initial surface admits a regular homotopy to a round sphere whose Willmore energy does not exceed that of the initial surface. This yields a classification of initial surfaces with energy at most 12 π $ 12\\pi $ 12 pi that lead to unavoidable singularities. As a further consequence, we obtain an extension of the Li–Yau inequality at 12 π $ 12\\pi $ 12 pi for a large class of immersed spheres without triple points. To prove these results, we glue together different instances of the Willmore flow and employ an invariant for triple-point-free immersed spheres.",
  "abstract_shown": true,
  "affiliations": [
    "Freie Universität Berlin",
    "Technical University Darmstadt"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Elena Mäder-Baumdicker",
      "orcid": "0000-0001-8125-8799"
    },
    {
      "affs": [
        1
      ],
      "name": "Jona Seidel",
      "orcid": "0009-0000-1282-8209"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/frvbjzgktjd74.bib",
  "cited_by": 0,
  "doi": "10.1017/fms.2026.10282",
  "fulltext_url": null,
  "id": "frvbjzgktjd74",
  "issns": [
    "2050-5094"
  ],
  "landing_url": "https://www.cambridge.org/core/product/identifier/S2050509426102825/type/journal_article",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
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  "openalex": "W4416513701",
  "pdf_url": "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3A045FCEB7F18D10516A1AD474E5873D/S2050509426102825a.pdf/div-class-title-the-willmore-energy-landscape-of-spheres-and-avoidable-singularities-of-the-willmore-flow-div.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": "Cambridge University Press (CUP)",
  "ris": "https://research.draconitic.com/paper/frvbjzgktjd74.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "10.1017/fms.2026.10282",
      "source": "crossref",
      "url": "https://www.cambridge.org/core/product/identifier/S2050509426102825/type/journal_article"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Geometric Analysis and Curvature Flows",
      "subfield": "general"
    }
  ],
  "title": "The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow",
  "title_text": "The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/frvbjzgktjd74",
  "venue": "Forum of Mathematics, Sigma",
  "versions": []
}