{"paper":{"title":"Capillary Christoffel-Minkowski problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.MG"],"primary_cat":"math.DG","authors_text":"Julian Scheuer, Mohammad N. Ivaki, Yingxiang Hu","submitted_at":"2025-04-12T19:47:26Z","abstract_excerpt":"The result of Guan and Ma (Invent. Math. 151 (2003)) states that if $\\phi^{-1/k} : \\mathbb{S}^n \\to (0,\\infty)$ is spherically convex, then $\\phi$ arises as the $\\sigma_k$ curvature (the $k$-th elementary symmetric function of the principal radii of curvature) of a strictly convex hypersurface. In this paper, we establish an analogous result in the capillary setting in the half-space for $\\theta\\in(0,\\pi/2)$: if $\\phi^{-1/k} : \\mathcal{C}_{\\theta} \\to (0,\\infty)$ is a capillary function and spherically convex, then $\\phi$ is the $\\sigma_k$ curvature of a strictly convex capillary hypersurface."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.09320","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/2504.09320/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"}