{
  "abstract": "We relate the hyperbolicity of a calibrated manifold $(X, ϕ)$ to the analytic properties of the space of Smith immersions $\\mathrm{SmIm}(B^k, X)$ from the Poincare $k$-ball into $X$. In particular, we establish the following calibrated analogue of a theorem of Royden: if $X$ is $ϕ$-saturated, then $R_ϕ$- and $K_ϕ$-hyperbolicity coincide, and either implies the equicontinuity of $\\mathrm{SmIm}(B^k, X)$ with respect to the $ϕ$-distance. This yields a Montel theorem for compact $ϕ$-saturated calibrated manifolds as an immediate corollary. Our primary technical tool is a new Schwarz lemma for Smith immersions from $B^k$ into $X$, which is of independent interest. In a similar spirit, we also prove a calibrated analogue of Kiernan's theorem to the effect that the $K_ϕ$-hyperbolicity of $X$ is almost equivalent to $\\mathrm{SmIm}(B^k, X)$ being a normal family. Finally, we prove that bounded domains in flat euclidean space are $R_ϕ$-hyperbolic for any calibration $ϕ$, and we investigate the hyperbolicity of products and discrete quotients.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.31393",
  "author_total": 3,
  "authors": [
    {
      "name": "Anton Iliashenko"
    },
    {
      "name": "Spiro Karigiannis"
    },
    {
      "name": "Jesse Madnick"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4h18pmce76rwq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.31393",
  "fulltext_url": null,
  "id": "4h18pmce76rwq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.31393",
  "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",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7166882304",
  "pdf_url": "https://arxiv.org/pdf/2606.31393",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4h18pmce76rwq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2606.31393",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.31393"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Montel's theorem and tautness in calibrated geometry",
  "title_text": "Montel's theorem and tautness in calibrated geometry",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/4h18pmce76rwq",
  "venue": "arXiv",
  "versions": []
}