{"paper":{"title":"Energy identity and removable singularities of maps from a Riemann surface with tension field unbounded in $L^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Yong Luo","submitted_at":"2011-10-21T20:26:02Z","abstract_excerpt":"We prove the removal singularity results for maps with bounded energy from the unit disk $B$ of $R^2$ centered at the origin to a closed Riemannian manifold whose tension field is unbounded in $L^2(B)$ but satisfies the following condition: {eqnarray*}\n  (\\int_{B_t\\setminus B_{\\frac{t}{2}}}|\\tau(u)|^2)^1/2\\leq C_1(\\frac{1}{t})^a, {eqnarray*} for some $0<a<1$ and for any $0<t<1$, where $C_1$ is a constant independent of $t$.\n  We will also prove that if a sequence $\\{u_n\\}$ has uniformly bounded energy and satisfies {eqnarray*}\n  (\\int_{B_t\\setminus B_{\\frac{t}{2}}}|\\tau(u_n)|^2)^1/2\\leq C_2(\\f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4901","kind":"arxiv","version":5},"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"}