{
  "abstract": "Let $M_f$ be the closed hyperbolic $3$--manifold which is the mapping torus of a pseudo-Anosov homeomorphism $f$ of a closed surface $S$ of genus at least two. The inclusion of the fiber subgroup \\(π_1(S)\\hookrightarrow π_1(M_f)\\) has a Cannon--Thurston boundary map \\(\\partialπ_1(S)\\cong S^1\\to S^2\\cong\\partialπ_1(M_f)\\), which is a Peano curve. We relate this map to two variational representatives of the fiber homotopy class: the harmonic map of Eells--Sampson and Hartman, and a least-area embedded minimal surface. Equivariant lifts of homotopic maps are a bounded distance apart; hence, for every marked conformal structure on $S$, the lift of the harmonic representative extends continuously to the closed disk with boundary value the Cannon--Thurston map, and a least-area fiber lifts to a properly embedded minimal plane in $\\Hh^3$ with the same boundary map. We give area and curvature bounds for a least-area fiber, show that its largest principal curvature is at least one, and study the energy of the harmonic representatives as a function on Teichmüller space, its critical points, which are the zeros of the Hopf differential, and its invariance under the monodromy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35858",
  "author_total": 1,
  "authors": [
    {
      "name": "Alberto Verjovsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/afnpra9tg4gc8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35858",
  "fulltext_url": null,
  "id": "afnpra9tg4gc8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35858",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7214899693",
  "pdf_url": "https://arxiv.org/pdf/2609.35858",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/afnpra9tg4gc8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.35858",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35858"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Cannon-Thurston Maps, Harmonic Maps, and Minimal Surfaces in Fibered Hyperbolic 3-Manifolds",
  "title_text": "Cannon-Thurston Maps, Harmonic Maps, and Minimal Surfaces in Fibered Hyperbolic 3-Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/afnpra9tg4gc8",
  "venue": "arXiv",
  "versions": []
}