{"paper":{"title":"Blowup behavior of harmonic maps with finite index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Lei Liu, Youde Wang, Yuxiang Li","submitted_at":"2015-12-18T14:27:00Z","abstract_excerpt":"In this paper, we study the blow-up phenomena on the $\\alpha_k$-harmonic map sequences with bounded uniformly $\\alpha_k$-energy, denoted by $\\{u_{\\alpha_k}: \\alpha_k>1 \\quad \\mbox{and} \\quad \\alpha_k\\searrow 1\\}$, from a compact Riemann surface into a compact Riemannian manifold. If the Ricci curvature of the target manifold is of a positive lower bound and the indices of the $\\alpha_k$-harmonic map sequence with respect to the corresponding $\\alpha_k$-energy are bounded, then, we can conclude that, if the blow-up phenomena occurs in the convergence of $\\{u_{\\alpha_k}\\}$ as $\\alpha_k\\searrow 1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05970","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"}