{"paper":{"title":"Hamiltonian stationary cones with isotropic links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jingyi Chen, Yu Yuan","submitted_at":"2017-04-18T22:27:40Z","abstract_excerpt":"We show that any closed oriented immersed Hamiltonian stationary isotropic surface $\\Sigma$ with genus $g_{\\Sigma}$ in $S^{5}\\subset\\mathbb{C}^{3}$ is (1) Legendrian and minimal if $g_{\\Sigma}=0$; (2) either Legendrian or with exactly $2g_{\\Sigma}-2$ Legendrian points if $g_{\\Sigma}\\geq1.$ In general, every compact oriented immersed isotropic submanifold $L^{n-1}\\subset S^{2n-1}\\subset\\mathbb{C}^{n}$ such that the cone $C\\left( L^{n-1}\\right) $ is Hamiltonian stationary must be Legendrian and minimal if its first Betti number is zero. Corresponding results for non-orientable links are also pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05553","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":""},"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"}