{"paper":{"title":"Montel's theorem and tautness in calibrated geometry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Anton Iliashenko, Jesse Madnick, Spiro Karigiannis","submitted_at":"2026-06-30T09:21:03Z","abstract_excerpt":"We relate the hyperbolicity of a calibrated manifold $(X, \\phi)$ 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 $\\phi$-replete, then $R_\\phi$- and $K_\\phi$-hyperbolicity coincide, and either implies the equicontinuity of $\\mathrm{SmIm}(B^k, X)$ with respect to the $\\phi$-distance. This yields a Montel theorem for compact $\\phi$-replete calibrated manifolds as an immediate corollary. Our primary technical tool is a new Schwarz "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31393","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.31393/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}