The classification of singly periodic minimal surfaces with genus zero and Scherk-type ends

DOI10.1090/S0002-9947-06-04094-3zbMath1110.53008OpenAlexW1740820649MaRDI QIDQ3420259

Martin Traizet, Joaquín Pérez

Publication date: 1 February 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-06-04094-3

zbMATH Keywords

minimal surfaces

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10)

Related Items (13)

Minimal surfaces in the three-sphere by desingularizing intersecting Clifford tori ⋮ A remark on limits of triply periodic minimal surfaces of genus 3 ⋮ Symmetry of some entire solutions to the Allen-Cahn equation in two dimensions ⋮ Gluing Karcher-Scherk saddle towers. I: Triply periodic minimal surfaces ⋮ Saddle towers and minimal k-noids in ℍ² × ℝ ⋮ On limits of triply periodic minimal surfaces ⋮ The space of 4-ended solutions to the Allen-Cahn equation in the plane ⋮ A characterisation of the Hoffman-Wohlgemuth surfaces in terms of their symmetries ⋮ The classical theory of minimal surfaces ⋮ Multiple end solutions to the Allen-Cahn equation in \(\mathbb{R}^2\) ⋮ Nondegeneracy of the saddle solution of the Allen-Cahn equation ⋮ Minimal surfaces with the area growth of two planes: The case of infinite symmetry ⋮ A new deformation family of Schwarz’ D surface

Cites Work

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• Topology and curvature of minimal surfaces properly embedded in \(\mathbb{R}^ 3\)
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• Uniqueness of the Riemann minimal examples
• Some existence and uniqueness theorems for doubly periodic minimal surfaces
• The geometry of periodic minimal surfaces
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• An embedded minimal surface with no symmetries
• Classification of doubly-periodic minimal surfaces of genus zero
• Embedded minimal surfaces: Forces, topology and symmetries
• The uniqueness of the helicoid
• The minimal lamination closure theorem
• Variational problems of minimal surface type. II: Boundary value problems for the minimal surface equation
• On embedded complete minimal surfaces of genus zero
• The space of properly embedded minimal surfaces and their Fourier transforms

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