{"paper":{"title":"Equipartition of several measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO"],"primary_cat":"math.MG","authors_text":"R.N. Karasev","submitted_at":"2010-11-22T10:08:02Z","abstract_excerpt":"We prove several results of the following type: any $d$ measures in $\\mathbb R^d$ can be partitioned simultaneously into $k$ equal parts by a convex partition (this particular result is proved independently by Pablo Sober\\'on). Another example is: Any convex body in the plane can be partitioned into $q$ parts of equal areas and perimeters provided $q$ is a prime power.\n  The above results give a partial answer to several questions posed by A. Kaneko, M. Kano, R. Nandakumar, N. Ramana Rao, and I. B\\'{a}r\\'{a}ny. The proofs in this paper are inspired by the generalization of the Borsuk--Ulam the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4762","kind":"arxiv","version":7},"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"}