{"paper":{"title":"Hyperplane conjecture for quotient spaces of $L_p$","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marius Junge","submitted_at":"1993-12-22T16:45:41Z","abstract_excerpt":"We give a positive solution for the hyperplane conjecture of quotient spaces F of $L_p$, where $1<p\\kll\\infty$. \\[ vol(B_F)^{\\frac{n-1}{n}} \\kl c_0 \\pl p' \\pl \\sup_{H \\p hyperplane} vol(B_F\\cap H) \\pl.\\] This result is extended to Banach lattices which does not contain $\\ell_1^n$'s uniformly. Our main tools are tensor products and minimal volume ratio with respect to $L_p$-sections."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9312207","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/math/9312207/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"}