{"paper":{"title":"On the polar Orlicz-Minkowski problems and the $p$-capacitary Orlicz-Petty bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Baocheng Zhu, Deping Ye, Xiaokang Luo","submitted_at":"2018-02-21T19:57:06Z","abstract_excerpt":"In this paper, we propose and study the polar Orlicz-Minkowski problems: under what conditions on a nonzero finite measure $\\mu$ and a continuous function $\\varphi:(0,\\infty)\\rightarrow(0,\\infty)$, there exists a convex body $K\\in\\mathcal{K}_0$ such that $K$ is an optimizer of the following optimization problems: \\begin{equation*} \\inf/\\sup \\bigg\\{\\int_{S^{n-1}}\\varphi\\big( h_L \\big) \\,d \\mu: L \\in \\mathcal{K}_{0} \\ \\text{and}\\ |L^\\circ|=\\omega_{n}\\bigg\\}. \\end{equation*} The solvability of the polar Orlicz-Minkowski problems is discussed under different conditions. In particular, under certai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07777","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"}