{"paper":{"title":"Uniqueness and non-uniqueness for the asymptotic Plateau problem in hyperbolic space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrea Seppi, Ben Lowe, Zheng Huang","submitted_at":"2023-09-01T17:35:14Z","abstract_excerpt":"We prove several results on the number of solutions to the asymptotic Plateau problem in $\\mathbb H^3$. Firstly we discuss criteria that ensure uniqueness. Given a Jordan curve $\\Lambda$ in the asymptotic boundary of $\\mathbb H^3$, we show that uniqueness of the minimal surfaces with asymptotic boundary $\\Lambda$ is equivalent to uniqueness in the smaller class of stable minimal disks. Then we show that if a quasicircle (or more generally, a Jordan curve of finite width) $\\Lambda$ is the asymptotic boundary of a minimal surface $\\Sigma$ with principal curvatures less than or equal to 1 in abso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.00599","kind":"arxiv","version":2},"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/2309.00599/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"}