{"paper":{"title":"Improvement of the Bernstein-type theorem for space-like zero mean curvature graphs in Lorentz-Minkowski space using fluid mechanical duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Kotaro Yamada, Masaaki Umehara, Shintaro Akamine","submitted_at":"2019-04-17T01:52:19Z","abstract_excerpt":"Calabi's Bernstein-type theorem asserts that a zero mean curvature entire graph in Lorentz-Minkowski space $\\boldsymbol L^3$ which admits only space-like points is a space-like plane. Using the fluid mechanical duality between minimal surfaces in Euclidean 3-space $\\boldsymbol E^3$ and maximal surfaces in Lorentz-Minkowski space $\\boldsymbol L^3$, we give an improvement of this Bernstein-type theorem. More precisely, we show that a zero mean curvature entire graph in $\\boldsymbol L^3$ which does not admit time-like points (namely, a graph consists of only space-like and light-like points) is a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08046","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"}