{"paper":{"title":"Minimal hypersurfaces in $\\mathbb{S}^{4}(1)$ by doubling the equatorial $\\mathbb{S}^{3}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jiahua Zou, Nikolaos Kapouleas","submitted_at":"2024-05-28T15:36:46Z","abstract_excerpt":"For each large enough $m\\in\\mathbb{N}$ we construct by PDE gluing methods a closed embedded smooth minimal hypersurface ${\\breve{M}_m}$ doubling the equatorial three-sphere $\\mathbb{S}_{\\mathrm{eq}}^3$ in $\\mathbb{S}^4(1)$, with ${\\breve{M}_m}$ containing $m^2$ bridges modelled after the three-dimensional catenoid and centered at the points of a square $m\\times m$ lattice $L$ contained in the Clifford torus $\\mathbb{T}^2\\subset \\mathbb{S}_{\\mathrm{eq}}^3$. This answers a long-standing question of Yau in the case of $\\mathbb{S}^4(1)$ and long-standing questions of Hsiang. Similarly we construct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.18283","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/2405.18283/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"}