{"paper":{"title":"Minimal surface system in Euclidean four-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Hojoo Lee","submitted_at":"2017-06-19T00:24:44Z","abstract_excerpt":"Generalizing the Cauchy-Riemann equations, we construct the Osserman system of the first order for a pair $\\left(f(x, y), g(x,y) \\right)$ of two ${\\mathbb{R}}$-valued functions on the domain $\\Omega \\subset {\\mathbb{R}}^{2}$. The graph $\\left\\{\\, \\left(x, y, f(x, y), g(x,y) \\right) \\in {\\mathbb{R}}^{4} \\, \\vert \\, (x,y) \\in \\Omega \\, \\right\\}$ becomes a minimal surface in ${\\mathbb{R}}^{4}$, whose generalized Gauss map lies on the intersection of a hyperplane of the complex projective space ${\\mathbb{CP}}^{3}$ and the complex cone ${z_1}^{2}+{z_2}^{2}+{z_3}^{2}+{z_4}^{2}=0$. We present two app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05751","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"}