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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2307.16484","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-07-31T08:29:33Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"26102277054c1042efa4ce931484909d6ad46244c534798fc6cd9c844bf00b7c","abstract_canon_sha256":"2ec69173fcdd671b8640a4b914450a0d4cdbae046cd21d3d6da17b4d2e0b1051"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:28:09.007829Z","signature_b64":"ZPIApYmUcOs1KYEq0O2xMRcRq77AaHU45pgqAlMIJifWtDgw6KQQyrkYrs5PYH6W8c3fEl2twWdxzKetZAeiBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"369b8f46266bf717a61ba93a0e3f81f7bfa15f24c09d06b48c5d56b74b95b9c7","last_reissued_at":"2026-07-05T11:28:09.007328Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:28:09.007328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $p \\geq p_\\gamma := 1 - \\frac{n+1}{\\gamma}$. 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