{
  "abstract": "In this paper, we study finite and infinite decomposition formulas for zero mean curvature (ZMC) graphs in Euclidean, Lorentz--Minkowski, and isotropic (3)-spaces. We first derive new Euler--Ramanujan-type identities that decompose the conjugate of Scherk's first minimal surface into dilated catenoids. Using Weierstrass factorisation and power series methods, we then obtain infinite decompositions for a broad class of isotropic ZMC graphs into helicoids, logarithmoids of revolution, and Enneper surfaces. These results are extended to wider families of ZMC surfaces arising from the López--Ros transformation, Bonnet rotation, and a one-parameter family of metric deformations. We also establish finite decomposition formulas, including analogues of Scherk tower decompositions in Euclidean and isotropic settings, and prove a characterisation theorem for finite decompositions of isotropic minimal surfaces. Finally, we discuss applications to lamellar structures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.11697",
  "author_total": 4,
  "authors": [
    {
      "name": "Priyank Vasu"
    },
    {
      "name": "Sam K Mathew"
    },
    {
      "name": "Rahul Kumar Singh"
    },
    {
      "name": "Rukmini Dey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1s2v6f8w144jc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.11697",
  "fulltext_url": null,
  "id": "1s2v6f8w144jc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.11697",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7164379518",
  "pdf_url": "https://arxiv.org/pdf/2606.11697",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1s2v6f8w144jc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2606.11697",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.11697"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Decompositions of ZMC Graphs and Euler-Ramanujan type identities",
  "title_text": "Decompositions of ZMC Graphs and Euler-Ramanujan type identities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/1s2v6f8w144jc",
  "venue": "arXiv",
  "versions": []
}