{"paper":{"title":"Remarks on the nonexistence of biharmonic maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Yong Luo","submitted_at":"2015-11-23T14:17:11Z","abstract_excerpt":"In this short note we study nonexistence result of biharmonic maps from a complete Riemannian manifold into a Riemannian manifold with nonpositive sectional curvature. Assume that $\\phi:(M,g)\\to (N, h)$ is a biharmonic map, where $(M, g)$ is a complete Riemannian manifold and $(N,h)$ a Riemannian manifold with nonpositive sectional curvature, we will prove that $\\phi$ is a harmonic map if one of the following conditions holds: (i) $|d\\phi|$ is bounded in $L^q(M)$ and $ \\int_M|\\tau(\\phi)|^pdv_g<\\infty, $ for some $1\\leq q\\leq\\infty$, $1< p<\\infty$; or (ii) $Vol(M)=\\infty$ and $ \\int_M|\\tau(\\phi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07231","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"}