{"paper":{"title":"Rigidity of inversive distance circle packings revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Xu Xu","submitted_at":"2017-05-08T00:31:38Z","abstract_excerpt":"Inversive distance circle packing metric was introduced by P Bowers and K Stephenson \\cite{BS} as a generalization of Thurston's circle packing metric \\cite{T1}. They conjectured that the inversive distance circle packings are rigid. For nonnegative inversive distance, Guo \\cite{Guo} proved the infinitesimal rigidity and then Luo \\cite{L3} proved the global rigidity. In this paper, based on an observation of Zhou \\cite{Z}, we prove this conjecture for inversive distance in $(-1, +\\infty)$ by variational principles. We also study the global rigidity of a combinatorial curvature introduced in \\c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02714","kind":"arxiv","version":4},"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"}