{"paper":{"title":"$L^p$-Minkowski Problem under Curvature Pinching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DG","authors_text":"Emanuel Milman, Mohammad N. Ivaki","submitted_at":"2023-07-31T08:29:33Z","abstract_excerpt":"Let $K$ be a smooth, origin-symmetric, strictly convex body in $\\mathbb{R}^n$. If for some $\\ell\\in GL(n,\\mathbb{R})$, the anisotropic Riemannian metric $\\frac{1}{2}D^2 \\Vert\\cdot\\Vert_{\\ell K}^2$, encapsulating the curvature of $\\ell K$, is comparable to the standard Euclidean metric of $\\mathbb{R}^{n}$ up-to a factor of $\\gamma > 1$, we show that $K$ satisfies the even $L^p$-Minkowski inequality and uniqueness in the even $L^p$-Minkowski problem for all $p \\geq p_\\gamma := 1 - \\frac{n+1}{\\gamma}$. This result is sharp as $\\gamma \\searrow 1$ (characterizing centered ellipsoids in the limit) a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.16484","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.16484/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"}