{"paper":{"title":"A local uniqueness theorem for minimizers of Petty's conjectured projection inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Mohammad N. Ivaki","submitted_at":"2016-10-12T17:33:36Z","abstract_excerpt":"Employing the inverse function theorem on Banach spaces, we prove that in a $C^{2}(S^{n-1})$-neighborhood of the unit ball, the only solutions of $\\Pi^2K=cK$ are origin-centered ellipsoids. Here $K$ is an $n$-dimensional convex body, $\\Pi K$ is the projection body of $K$ and $\\Pi^2K=\\Pi(\\Pi K).$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03796","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"}