{"paper":{"title":"On the small measure expansion phenomenon in connected noncompact nonabelian groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Chieu-Minh Tran, Jinpeng An, Ruixiang Zhang, Yifan Jing","submitted_at":"2021-11-09T16:16:01Z","abstract_excerpt":"Suppose $G$ is a connected noncompact locally compact group, $A,B$ are nonempty and compact subsets of $G$, $\\mu$ is a left Haar measure on $G$. Assuming that $G$ is unimodular, and $ \\mu(A^2) < K \\mu(A) $ with $K>1$ a fixed constant, our first result shows that there is a continuous surjective group homomorphism $\\chi: G\\to L$ with compact kernel, where $L$ is a Lie group with $$\\dim(L) \\leq \\lfloor\\log K\\rfloor(\\lfloor\\log K\\rfloor+1)/2.$$ We also demonstrate that this dimension bound is sharp, establish the relationship between $A$ and its image under the quotient map, and obtain a more gen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.05236","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.05236/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}