{"paper":{"title":"Complex Lagrangian minimal surfaces, bi-complex Higgs bundles and $\\mathrm{SL}(3,\\mathbb{C})$-quasi-Fuchsian representations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT","math.SG"],"primary_cat":"math.DG","authors_text":"Andrea Tamburelli, Nicholas Rungi","submitted_at":"2024-06-21T07:57:44Z","abstract_excerpt":"In this paper we introduce complex minimal Lagrangian surfaces in the bi-complex hyperbolic space and study their relation with representations in $\\mathrm{SL}(3,\\mathbb{C})$. Our theory generalizes at the same time minimal Lagrangian surfaces in the complex hyperbolic plane, hyperbolic affine spheres in $\\mathbb{R}^3$, and Bers embeddings in the holomorphic space form $\\mathbb{CP}^1 \\times \\mathbb{CP}^1 \\setminus \\Delta$. If these surfaces are equivariant under representations in $\\mathrm{SL}(3,\\mathbb{C})$, our approach generalizes the study of almost $\\mathbb{R}$-Fuchsian representations in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.14945","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/2406.14945/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"}