{"paper":{"title":"Spacelike convex surfaces with prescribed curvature in (2+1)-Minkowski space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.GT"],"primary_cat":"math.DG","authors_text":"Andrea Seppi, Francesco Bonsante","submitted_at":"2015-05-25T20:25:42Z","abstract_excerpt":"We prove existence and uniqueness of solutions to the Minkowski problem in any domain of dependence $D$ in $(2+1)$-dimensional Minkowski space, provided $D$ is contained in the future cone over a point. Namely, it is possible to find a smooth convex Cauchy surface with prescribed curvature function on the image of the Gauss map. This is related to solutions of the Monge-Amp\\`ere equation $\\det D^2 u(z)=(1/\\psi(z))(1-|z|^2)^{-2}$ on the unit disc, with the boundary condition $u|_{\\partial\\mathbb{D}}=\\varphi$, for $\\psi$ a smooth positive function and $\\varphi$ a bounded lower semicontinuous fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06748","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"}