{"paper":{"title":"Unstable minimal surfaces in symmetric spaces of non-compact type","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Nathaniel Sagman, Peter Smillie","submitted_at":"2022-08-09T16:27:32Z","abstract_excerpt":"We prove that if $\\Sigma$ is a closed surface of genus at least 3 and $G$ is a split real semisimple Lie group of rank at least $3$ acting faithfully by isometries on a symmetric space $N$, then there exists a Hitchin representation $\\rho:\\pi_1(\\Sigma)\\to G$ and a $\\rho$-equivariant unstable minimal map from the universal cover of $\\Sigma$ to $N$. This follows from a new lower bound on the index of high energy minimal maps into an arbitrary symmetric space of non-compact type. Taking $G=\\mathrm{PSL}(n,\\mathbb{R})$, $n\\geq 4$, this disproves the Labourie conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.04885","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/2208.04885/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"}