{"paper":{"title":"Submanifolds of warped product manifolds $I\\times_f S^{m-1}(k)$}} from a $p$-harmonic viewpoint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bang-Yen Chen, Shihshu Walter Wei","submitted_at":"2013-07-07T15:22:14Z","abstract_excerpt":"We study $p$-harmonic maps, $p$-harmonic morphisms, biharmonic maps, and quasiregular mappings into submanifolds of warped product Riemannian manifolds ${I}\\times_f S^{m-1}(k)\\, $ of an open interval and a complete simply-connecteded $(m-1)$-dimensional Riemannian manifold of constant sectional curvature $k$. We establish an existence theorem for $p$-harmonic maps and give a classification of complete stable minimal surfaces in certain three dimensional warped product Riemannian manifolds ${\\bf R}\\times_f S^{2}(k)\\, ,$ building on our previous work. When $f \\equiv\\, $ Const. and $k=0$, we reca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1876","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":""},"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"}