{"paper":{"title":"Energy identity for stationary biharmonic mappings into spheres in supercritical dimensions","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"Stationary biharmonic maps into spheres satisfy an energy identity when the domain dimension is at least five.","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Chang-Lin Xiang, Changyou Wang, Chang-Yu Guo","submitted_at":"2026-05-13T19:19:21Z","abstract_excerpt":"Energy identity for harmonic type maps in supercritical dimensions is an important and difficult problem. For sphere-valued harmonic maps, the first breakthrough was achieved by Lin-Rivi\\`ere [Duke Math. J. 2002]. In this paper, by adapting their strategy, we establish the energy identity for stationary biharmonic maps into spheres in supercritical dimensions $n\\ge 5$."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we establish the energy identity for stationary biharmonic maps into spheres in supercritical dimensions n≥5","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The maps are stationary biharmonic and the dimension satisfies n≥5; the adaptation of the Lin-Rivière strategy succeeds without further restrictions on the maps or domain.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Establishes the energy identity for stationary biharmonic maps into spheres in supercritical dimensions n ≥ 5.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Stationary biharmonic maps into spheres satisfy an energy identity when the domain dimension is at least five.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"fbfd3a7cb339a205f04736e0f3200f57fcf73b39228e59aec6826180d6496f68"},"source":{"id":"2605.14052","kind":"arxiv","version":1},"verdict":{"id":"3cfb53e2-743c-4094-b1a7-46f6cb5af425","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:44:46.182100Z","strongest_claim":"we establish the energy identity for stationary biharmonic maps into spheres in supercritical dimensions n≥5","one_line_summary":"Establishes the energy identity for stationary biharmonic maps into spheres in supercritical dimensions n ≥ 5.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The maps are stationary biharmonic and the dimension satisfies n≥5; the adaptation of the Lin-Rivière strategy succeeds without further restrictions on the maps or domain.","pith_extraction_headline":"Stationary biharmonic maps into spheres satisfy an energy identity when the domain dimension is at least five."},"references":{"count":37,"sample":[{"doi":"","year":2008,"title":"De Lellis , Rectifiable sets, densities and tangent measures","work_id":"9bc5ddea-5ad9-44b0-bef1-f71650632f1c","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"S. Y. A. Chang, L. Wang and P. C. Yang, A regularity theory of biharmonic maps. Commun. Pure Appl. Math. 52(9) (1999), 1113-1137","work_id":"69046ce1-fea9-498d-a9be-f4c776e69926","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Y. Chen and M. Zhu , Bubbling analysis for extrinsic biharmonic maps from general Riemannian 4-manifolds. Sci. China Math. 66 (2023), no. 3, 581-600","work_id":"de5ba0dc-613b-453d-8482-e17c89a0e3e6","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1991,"title":"C. L. Evans, Partial regularity for stationary harmonic maps into spheres. Arch. Rat. Mech. Anal. 116 (1991), 101-163","work_id":"ff0e57b1-bae0-420c-9a87-84bd27f9123d","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1995,"title":"W. Y. Ding and G. Tian , Energy identity for a class of approximate harmonic maps from surfaces. Comm. Anal. Geom. 3 (1995), 543-554","work_id":"d0b73d52-3b4d-454f-b588-604a3f320f9a","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":37,"snapshot_sha256":"c95c7fa45b011ebf514e8a587a8b5ac819a46b1bd5a2853bdf75c7ec4206b946","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"}