{"paper":{"title":"Rotation invariant singular K\\\"ahler metrics with constant scalar curvature on $\\mathbb{C}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA","math.CV"],"primary_cat":"math.DG","authors_text":"Jun Li, Weiyong He","submitted_at":"2018-08-12T11:38:45Z","abstract_excerpt":"The scalar curvature equation for rotation invariant K\\\"ahler metrics on $\\mathbb{C}^n \\backslash \\{0\\}$ is reduced to a system of ODEs of order 2. By solving the ODEs, we obtain complete lists of rotation invariant zero or positive csck on $\\mathbb{C}^n \\backslash \\{0\\}$ in lower dimensions. We also prove that there does not exist negative csck on $\\mathbb{C}^n \\backslash \\{0\\}$ for $n=2,3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03925","kind":"arxiv","version":3},"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"}