{"paper":{"title":"Links between different analytic descriptions of constant mean curvature surfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alfred M. Grundland, Eugene V. Ferapontov","submitted_at":"2000-01-01T00:00:00Z","abstract_excerpt":"Transformations between different analytic descriptions of constant mean curvature (CMC) surfaces are established. In particular, it is demonstrated that the system \\[ \\begin{split} &\\partial \\psi_{1} = (|\\psi_{1}|^{2} + |\\psi_{2}|^{2}) \\psi_{2} \\\\ &\\bar{\\partial} \\psi_{2} =- (|\\psi_{1}|^{2} + |\\psi_{2}|^{2}) \\psi_{1} \\end{split} \\] descriptive of CMC surfaces within the framework of the generalized Weierstrass representation, decouples into a direct sum of the elliptic Sh-Gordon and Laplace equations. Connections of this system with the sigma model equations are established. It is pointed out"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0001189","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"}