{"paper":{"title":"Existence and asymptotics for solutions of a non-local Q-curvature equation in dimension three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ali Maalaoui, Jingang Xiong, Luca Martinazzi, Tianling Jin","submitted_at":"2013-09-17T13:24:28Z","abstract_excerpt":"We study conformal metrics on $R^3$, i.e., metrics of the form $g_u=e^{2u}|dx|^2$, which have constant $Q$-curvature and finite volume. This is equivalent to studying the non-local equation $$ (-\\Delta)^\\frac32 u = 2 e^{3u}$$ in $R^3$ $$V:=\\int_{\\mathbb{R}^3}e^{3u}dx<\\infty,$$ where $V$ is the volume of $g_u$. Adapting a technique of A. Chang and W-X. Chen to the non-local framework, we show the existence of a large class of such metrics, particularly for $V\\le 2\\pi^2=|S^3|$. Inspired by previous works of C-S. Lin and L. Martinazzi, who treated the analogue cases in even dimensions, we classif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4299","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"}