{"paper":{"title":"Lorentzian area measures and the Christoffel problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Fran\\c{c}ois Fillastre, Giona Veronelli","submitted_at":"2013-02-25T17:35:45Z","abstract_excerpt":"We introduce a particular class of unbounded closed convex sets of $\\R^{d+1}$, called F-convex sets (F stands for future). To define them, we use the Minkowski bilinear form of signature $(+,...,+,-)$ instead of the usual scalar product, and we ask the Gauss map to be a surjection onto the hyperbolic space $\\H^d$. Important examples are embeddings of the universal cover of so-called globally hyperbolic maximal flat Lorentzian manifolds.\n  Basic tools are first derived, similarly to the classical study of convex bodies. For example, F-convex sets are determined by their support function, which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6169","kind":"arxiv","version":2},"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"}