{"paper":{"title":"Uniqueness of Lp Minkowski problem in the supercritical range","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shi-Zhong Du","submitted_at":"2025-04-09T14:53:18Z","abstract_excerpt":"The uniqueness of the $L_p$-Minkowski problem has been a long standing problem in convex geometry, which draws back earlier in 1974 the paper (Mathematika, {\\bf21}, 1974) by Firey, and later developed by Lutwak, Yang, Zhang (Trans. Am. Math. Soc., {\\bf356}, 2004) et al. In the groundbreaking paper by Brendle-Choi-Daskalopoulos (Acta Math, {\\bf219}, 2017), a full uniqueness result was shown for the subcritical exponents $p\\in(-n-1,1]$. In the supercritical range, the uniqueness problem is much more complicated, even on the planar case $n=1$. One of the famous results was shown by Andrews in (J."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.06946","kind":"arxiv","version":6},"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/2504.06946/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"}