{"paper":{"title":"General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski Problem II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG","math.FA"],"primary_cat":"math.MG","authors_text":"Daniel Hug, Deping Ye, Richard J. Gardner, Sudan Xing","submitted_at":"2018-09-25T23:14:07Z","abstract_excerpt":"The general dual volume $\\dveV(K)$ and the general dual Orlicz curvature measure $\\deV(K, \\cdot)$ were recently introduced for functions $G: (0, \\infty)\\times \\sphere\\rightarrow (0, \\infty)$ and convex bodies $K$ in $\\R^n$ containing the origin in their interiors. We extend $\\dveV(K)$ and $\\deV(K, \\cdot)$ to more general functions $G: [0, \\infty)\\times \\sphere\\rightarrow [0, \\infty)$ and to compact convex sets $K$ containing the origin (but not necessarily in their interiors). Some basic properties of the general dual volume and of the dual Orlicz curvature measure, such as the continuous depe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09753","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":""},"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"}