{"paper":{"title":"The $L_p$ dual Minkowski problem for unbounded closed convex sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.MG","authors_text":"Deping Ye, Wen Ai, Yunlong Yang","submitted_at":"2024-04-15T14:01:57Z","abstract_excerpt":"The central focus of this paper is the $L_p$ dual Minkowski problem for $C$-compatible sets, where $C$ is a pointed closed convex cone in $\\mathbb{R}^n$ with nonempty interior. Such a problem deals with the characterization of the $(p, q)$-th dual curvature measure of a $C$-compatible set. It produces new Monge-Amp\\`{e}re equations for unbounded convex hypersurface, often defined over open domains and with non-positive unknown convex functions. Within the family of $C$-determined sets, the $L_p$ dual Minkowski problem is solved for $0\\neq p\\in \\mathbb{R}$ and $q\\in \\mathbb{R}$; while it is sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.09804","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/2404.09804/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"}