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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1901.05664","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-17T07:51:32Z","cross_cats_sorted":[],"title_canon_sha256":"a23c5263fe153519dc0b2541df4f648c9b17aea65e77646177410306605c0898","abstract_canon_sha256":"d6e37b64bd8067be29c593fe866e4455ea1962c9da509367d2dc976f16859911"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:42.448187Z","signature_b64":"9q3vPlG0/8evnK/sxcRSyQntf8gtMlBfGfrdtrhIQJ8gUATh7Df2JpbJ0R41CzZJrECq0zrP6iAxEw2xDyqgCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e88ca6870675da6e6df956f2cedd26b8748a04cb5a0ed47690c09938453e9209","last_reissued_at":"2026-05-17T23:54:42.447662Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:42.447662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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