{"paper":{"title":"Rectangular constrained Willmore minimizers and the Willmore conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Cheikh Birahim Ndiaye, Lynn Heller, Sebastian Heller","submitted_at":"2019-01-17T07:51:32Z","abstract_excerpt":"We show that the well-known family of $2$-lobed Delaunay tori $\\;f^b\\;$ in $\\;S^3,\\;$ parametrized by $\\;b \\in \\mathbb R_{\\geq1},\\;$ uniquely minimizes the Willmore energy among all immersions from tori into $3$-space of conformal class $\\;(a, b)\\;$. As a corollary we obtain an alternate proof of the Willmore conjecture in $3$-space. This new strategy can be generalized to arbitrary codimensions provided a classification of isothermic constrained Willmore tori is possible and all $\\;f^b\\;$ remain stable in all codimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05664","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":""},"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"}