{"paper":{"title":"Local rigidity for hyperbolic groups with Sierpi\\'nski carpet boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Sergei Merenkov","submitted_at":"2013-07-06T15:19:09Z","abstract_excerpt":"Let $G$ and $\\tilde G$ be Kleinian groups whose limit sets $S$ and $\\tilde S$, respectively, are homeomorphic to the standard Sierpi\\'nski carpet, and such that every complementary component of each of $S$ and $\\tilde S$ is a round disc. We assume that the groups $G$ and $\\tilde G$ act cocompactly on triples on their respective limit sets. The main theorem of the paper states that any quasiregular map (in a suitably defined sense) from an open connected subset of $S$ to $\\tilde S$ is the restriction of a M\\\"obius transformation that takes $S$ onto $\\tilde S$, in particular it has no branching."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1792","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"}