{"paper":{"title":"Huisken-Yau-type uniqueness for area-constrained Willmore spheres","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Felix Schulze, Jan Metzger, Michael Eichmair, Thomas Koerber","submitted_at":"2022-04-08T14:41:32Z","abstract_excerpt":"Let $(M,g)$ be a Riemannian $3$-manifold that is asymptotic to Schwarzschild. We study the existence of large area-constrained Willmore spheres $\\Sigma \\subset M$ with non-negative Hawking mass and inner radius $\\rho$ dominated by the area radius $\\lambda$. If the scalar curvature of $(M,g)$ is non-negative, we show that no such surfaces with $\\log \\lambda \\ll \\rho$ exist. This answers a question of G. Huisken."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.04102","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/2204.04102/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"}