{
  "abstract": "Let $(M,g)$ be a closed Riemannian manifold of positive Ricci curvature. Let $f$ be a proper isoparametric function on $M$, and $Γ$ the unique level set of $f$ which is a minimal hypersurface. For any positive integer $k$, and $λ>0$ large enough, we construct a solution of the Allen-Cahn equation $ Δu + λ(u-u^3 ) =0$ which is constant along the level sets of $f$ and has exactly $k$ nodal components. We prove that the nodal components approach the minimal isoparametric hypersurface $Γ$ as $λ\\rightarrow \\infty$ and the energy is uniformly bounded for all such solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05715",
  "author_total": 2,
  "authors": [
    {
      "name": "Guillermo Henry"
    },
    {
      "name": "Jimmy Petean"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/03de3wx5595xy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05715",
  "fulltext_url": null,
  "id": "03de3wx5595xy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05715",
  "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"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212064231",
  "pdf_url": "https://arxiv.org/pdf/2609.05715",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/03de3wx5595xy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05715",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05715"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Interface foliation near a minimal isoparametric hypersurface for the Allen-Cahn equation",
  "title_text": "Interface foliation near a minimal isoparametric hypersurface for the Allen-Cahn equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/03de3wx5595xy",
  "venue": "arXiv",
  "versions": []
}