{"paper":{"title":"On the conformal dimension of product measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CA","authors_text":"David Bate, Tuomas Orponen","submitted_at":"2017-04-24T13:34:38Z","abstract_excerpt":"Given a compact set $E \\subset \\mathbb{R}^{d - 1}$, $d \\geq 1$, write $K_{E} := [0,1] \\times E \\subset \\mathbb{R}^{d}$. A theorem of C. Bishop and J. Tyson states that any set of the form $K_{E}$ is minimal for conformal dimension: if $(X,d)$ is a metric space and $f \\colon K_{E} \\to (X,d)$ is a quasisymmetric homeomorphism, then $$\\dim_{\\mathrm{H}} f(K_{E}) \\geq \\dim_{\\mathrm{H}} K_{E}.$$ We prove that the measure-theoretic analogue of the result is not true. For any $d \\geq 2$ and $0 \\leq s < d - 1$, there exist compact sets $E \\subset \\mathbb{R}^{d - 1}$ with $0 < \\mathcal{H}^{s}(E) < \\inft"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07215","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"}