{"paper":{"title":"Conformally Euclidean metrics on $\\mathbb{R}^n$ with arbitrary total $Q$-curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ali Hyder","submitted_at":"2016-08-05T15:05:42Z","abstract_excerpt":"We study the existence of solution to the problem $$(-\\Delta)^\\frac n2u=Qe^{nu}\\quad\\text{in }\\mathbb{R}^{n},\\quad \\kappa:=\\int_{\\mathbb{R}^{n}}Qe^{nu}dx<\\infty,$$ where $Q\\geq 0$, $\\kappa\\in (0,\\infty)$ and $n\\geq 3$. Using ODE techniques Martinazzi for $n=6$ and Huang-Ye for $n=4m+2$ proved the existence of solution to the above problem with $Q\\equiv const>0$ and for every $\\kappa\\in (0,\\infty)$. We extend these results in every dimension $n\\geq 5$, thus completely answering the problem opened by Martinazzi. Our approach also extends to the case in which $Q$ is non-constant, and under some d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01905","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"}