{"paper":{"title":"Quasisymmetric rigidity of Sierpinski carpets $F_{n,p}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CV","authors_text":"Jinsong Zeng, Weixu Su","submitted_at":"2013-04-08T00:03:46Z","abstract_excerpt":"We study a new class of square Sierpi\\'nski carpets $F_{n,p}$ ($5\\leq n, 1\\leq p<\\frac{n}{2}-1$) on $\\mathbb{S}^2$, which are not quasisymmetrically equivalent to the standard Sierpi\\'{n}ski carpets. We prove that the group of quasisymmetric self-maps of each $F_{n,p}$ is the Euclidean isometry group.\n  We also establish that $F_{n,p}$ and $F_{n',p'}$ are quasisymmetrically equivalent if and only if $(n,p)=(n',p')$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2078","kind":"arxiv","version":2},"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"}