{"paper":{"title":"On the general dual Orlicz-Minkowski problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.MG","authors_text":"Deping Ye, Sudan Xing","submitted_at":"2018-02-18T04:41:19Z","abstract_excerpt":"For $K\\subseteq \\mathbb{R}^n$ a convex body with the origin $o$ in its interior, and $\\phi:\\mathbb{R}^n\\setminus\\{o\\}\\rightarrow(0, \\infty)$ a continuous function, define the general dual ($L_{\\phi})$ Orlicz quermassintegral of $K$ by $$\\mathcal{V}_\\phi(K)=\\int_{\\mathbb{R}^n \\setminus K} \\phi(x)\\,dx.$$ Under certain conditions on $\\phi$, we prove a variational formula for the general dual ($L_{\\phi})$ Orlicz quermassintegral, which motivates the definition of $\\widetilde{C}_{\\phi,\\mathcal{V}}(K, \\cdot)$, the general dual ($L_{\\phi})$ Orlicz curvature measure of $K$.\n  We pose the following gen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06331","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"}