{
  "abstract": "In this paper we study the global geometry and classification of complete minimal surfaces with embedded ends and finite total curvature in the product space $\\mathbb{H}^2 \\times \\mathbb{R}$. We describe the structure of embedded ends of such surfaces, constraining the combinatorics of their asymptotic polygons at infinity. Focusing on small total curvature values, we establish a complete classification of the possible asymptotic boundaries for embedded minimal surfaces with total curvature $-4π$ and $-6π$. In the $-4π$ case, we prove the surface is either a horizontal catenoid or simply-connected, with asymptotic boundary belonging to one of four explicit configurations. In the $-6π$ case, we show that any embedded example must be simply-connected and classify its possible ideal boundaries. We further construct, via an asymptotic Plateau problem solved by area-minimizing surfaces and successive Schwarz reflections, new 1- and 2-parameter families of (possibly non-embedded) simply-connected minimal surfaces with total curvature $-6π$ (and, more generally, $-2(2k-1)π$) whose ends are embedded and realize asymptotic configurations not previously known to occur.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07885",
  "author_total": 2,
  "authors": [
    {
      "name": "Jesús Castro-Infantes"
    },
    {
      "name": "Magdalena Rodríguez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d7apt6kgj8gwq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07885",
  "fulltext_url": null,
  "id": "d7apt6kgj8gwq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07885",
  "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.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212080094",
  "pdf_url": "https://arxiv.org/pdf/2609.07885",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d7apt6kgj8gwq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07885",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07885"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Minimal surfaces in $\\mathbb{H}^2\\times\\mathbb{R}$ with finite total curvature and embedded ends",
  "title_text": "Minimal surfaces in ℍ^2×ℝ with finite total curvature and embedded ends",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/d7apt6kgj8gwq",
  "venue": "arXiv",
  "versions": []
}