{"paper":{"title":"Uniqueness of $S_2$-isotropic solutions to the isotropic $L_p$ Minkowski problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.MG"],"primary_cat":"math.DG","authors_text":"Yao Wan","submitted_at":"2025-09-10T13:33:42Z","abstract_excerpt":"This paper investigates the spectral properties of the Hilbert-Brunn-Minkowski operator $L_K$ to derive stability estimates for geometric inequalities, including the local Brunn-Minkowski inequality. By analyzing the eigenvalues of $L_K$, we establish the uniqueness of $S_2$-isotropic solutions to the isotropic $L_p$ Minkowski problem in $\\mathbb{R}^{n}$ for $\\frac{1-3n^2}{2n}\\leq p<-n$ with $\\lambda_2(-L_K)\\geq \\frac{n-1}{2n-1+p}$. Furthermore, we extend this uniqueness result to the range $-2n-1 \\leq p<-n$ with $\\lambda_2(-L_K)\\geq \\frac{-p-1}{n-1}$, assuming the origin-centred condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.08588","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/2509.08588/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"}