{"paper":{"title":"Lu's conjecture for minimal surfaces in codimension two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Fagui Li, Jianquan Ge, Yunheng Zhang","submitted_at":"2026-07-23T14:05:10Z","abstract_excerpt":"Let $M^2\\to\\Sph^4$ be a closed minimal immersion, let $S$ be the squared norm of its second fundamental form, and let $\\lambda_1\\geq\\lambda_2\\geq0$ be the eigenvalues of Lu's fundamental matrix. We prove that if $S+\\lambda_2$ is constant and larger than $2$, then $S+\\lambda_2\\geq3$. Thus Lu's second-gap conjecture holds for minimal surfaces in codimension two.\n  Together with the hypersurface result of Peng--Terng and the counterexamples of Li--Zhao in every codimension $m\\geq3$, our theorem completes the codimension picture of Lu's second-gap conjecture for minimal surfaces: it holds precisel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21336","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/2607.21336/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"}