{"paper":{"title":"A nonexistence theorem for proper biharmonic maps into general Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Volker Branding, Yong Luo","submitted_at":"2018-06-28T08:09:24Z","abstract_excerpt":"In this note we prove a nonexistence result for proper biharmonic maps from complete non-compact Riemannian manifolds of dimension \\(m=\\dim M\\geq 3\\) with infinite volume that admit an Euclidean type Sobolev inequality into general Riemannian manifolds by assuming finiteness of $\\|\\tau(\\phi)\\|_{L^p(M)}, p>1$ and smallness of $\\|d\\phi\\|_{L^m(M)}$. This is an improvement of a recent result of the first named author, where he assumed $2<p<m$. As applications we also get several nonexistence results for proper biharmonic submersions from complete non-compact manifolds into general Riemannian manif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.11441","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"}