{"paper":{"title":"Heat flow method to Lichnerowicz type equation on closed manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Li Ma, Yuhua Sun","submitted_at":"2010-02-27T03:56:31Z","abstract_excerpt":"In this paper, we establish existence results for positive solutions to the Lichnerowicz equation of the following type in closed manifolds -\\Delta u=A(x)u^{-p}-B(x)u^{q},\\quad in\\quad M, where $p>1, q>0$, and $A(x)>0$, $B(x)\\geq0$ are given smooth functions. Our analysis is based on the global existence of positive solutions to the following heat equation {ll} u_t-\\Delta u=A(x)u^{-p}-B(x)u^{q},\\quad in\\quad M\\times\\mathbb{R}^{+}, u(x,0)=u_0,\\quad in\\quad M with the positive smooth initial data $u_0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.0053","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"}