On constant mean curvature surfaces with periodic metric

DOI10.2140/pjm.1998.182.229zbMath0906.53005OpenAlexW2121994045MaRDI QIDQ1392490

Josef F. Dorfmeister, Guido Haak

Publication date: 8 February 1999

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.1998.182.229

zbMATH Keywords

hyperelliptic curvesumbilicssinh-Gordon equationWeierstrass representationconstant mean curvature toriDPW methodtranslational symmetriesfinite type surfaces with periodic metric

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (9)

On the associated family of Delaunay surfaces ⋮ Construction of constant mean curvature \(n\)-noids using the DPW method ⋮ Finite type minimal annuli in \(\mathbb{S}^{2}\times\mathbb{R}\) ⋮ Construction of constant mean curvature \(n\)-noids from holomorphic potentials ⋮ Unitarization of Loop Group Representations of Fundamental Groups ⋮ Opening nodes in the DPW method: co-planar case ⋮ Dressing preserving the fundamental group ⋮ Coarse classification of constant mean curvature cylinders ⋮ Minimal surfaces with non-trivial geometry in the three-dimensional Heisenberg group

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