Helicoid-like minimal disks and uniqueness

DOI10.1515/CRELLE.2011.037zbMath1225.53008arXiv0802.1497MaRDI QIDQ5198584

Christine Breiner, Jacob Bernstein

Publication date: 8 August 2011

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.1497

zbMATH Keywords

minimal surfacegenushelicoidminimal disk

Mathematics Subject Classification ID

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

Related Items (8)

Evolution of form and shape ⋮ Embedded minimal surfaces of finite topology ⋮ Distortions of the helicoid ⋮ Generalizations of the Choe-Hoppe helicoid and Clifford cones in Euclidean space ⋮ Curvature estimates for constant mean curvature surfaces ⋮ Limit lamination theorem for H-disks ⋮ The embedded Calabi-Yau conjecture for finite genus ⋮ The classical theory of minimal surfaces

Cites Work

• Regularity of the singular set in the Colding-Minicozzi lamination theorem
• The strong halfspace theorem for minimal surfaces
• Distortions of the helicoid
• The space of embedded minimal surfaces of fixed genus in a 3-manifold. I: Estimates off the axis for disks
• The space of embedded minimal surfaces of fixed genus in a 3-manifold. II: Multi-valued graphs in disks
• The space of embedded minimal surfaces of fixed genus in a 3-manifold. III: Planar domains
• The space of embedded minimal surfaces of fixed genus in a 3-manifold. IV: Locally simply connected
• The uniqueness of the helicoid
• An embedded genus-one helicoid
• The Calabi-Yau conjectures for embedded surfaces
• Embedded minimal disks: Proper versus nonproper—global versus local
• Shapes of embedded minimal surfaces

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