{"paper":{"title":"On the deformation of inversive distance circle packings, III","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.GT","authors_text":"Huabin Ge, Wenshuai Jiang","submitted_at":"2017-09-28T09:42:55Z","abstract_excerpt":"Given a triangulated surface $M$, we use Ge-Xu's $\\alpha$-flow \\cite{Ge-Xu1} to deform any initial inversive distance circle packing metric to a metric with constant $\\alpha$-curvature. More precisely, we prove that the inversive distance circle packing with constant $\\alpha$-curvature is unique if $\\alpha\\chi(M)\\leq 0$, which generalize Andreev-Thurston's rigidity results for circle packing with constant cone angles. We further prove that the solution to Ge-Xu's $\\alpha$-flow can always be extended to a solution that exists for all time and converges exponentially fast to constant $\\alpha$-cu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09874","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"}