{"paper":{"title":"A note on the nonexistence of quasi-harmonic spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jiayu Li, Linlin Sun","submitted_at":"2016-04-10T14:37:00Z","abstract_excerpt":"In this paper we study the properties of quasi-harmonic spheres from $\\R^m, m>2$. We show that if the universal covering $\\tilde N$ of $N$ admits a nonnegative strictly convex function $\\rho$ with the exponential growth condition $\\rho(y)\\leq C\\exp\\left(\\frac14\\tilde d(y)^{2/m}\\right)$ where $\\tilde d(y)$ is the distance function on $\\tilde N$, then $N$ does not admit a quasi-harmonic sphere, which generalize Li-Zhu's result \\cite{Li2010non}. We also show that if $u$ is a quasi-harmonic sphere, then the property that $u$ is of finite energy ($\\int_{\\R^m}e(u)e^{-\\abs{x}^2/4}\\dif x<\\infty$) is e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02696","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"}