{"paper":{"title":"Bernstein-type theorem for stationary hypersurfaces of the Euler-Dierkes-Huisken functional","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hongbin Cui, Jiahuan Li, Xiaowei Xu","submitted_at":"2026-06-29T09:14:12Z","abstract_excerpt":"We say that a hypersurface $\\Sigma \\subset\\mathbb{R}^{n+1}$ is $\\alpha$-stationary if it is a critical point of the Euler-Dierkes-Huisken functional $\\mathcal{E}_\\alpha(\\Sigma)=\\int_\\Sigma|X|^\\alpha\\, d\\mathcal{H}^n$, introduced by Dierkes and Huisken in \\cite{[DH-24]}. In this paper, we prove that every smooth, complete, connected, embedded $\\alpha$-stationary hypersurface in $\\mathbb{R}^{n+1}$ passing through the origin with $\\alpha>0$ is a linear hyperplane."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30008","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.30008/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"}