Shapes of embedded minimal surfaces

DOI10.1073/pnas.0510379103zbMath1175.53008OpenAlexW1981175365WikidataQ34983810 ScholiaQ34983810MaRDI QIDQ5385891

Tobias Holck Colding, William P. II. Minicozzi

Publication date: 7 May 2008

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1073/pnas.0510379103

zbMATH Keywords

diskhelicoidcatenoid

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10)

Related Items (20)

Embedded plateau problem ⋮ Self-shrinkers with a rotational symmetry ⋮ Uniqueness of self-similar shrinkers with asymptotically conical ends ⋮ Two-point functions and their applications in geometry ⋮ Locally helical surfaces have bounded twisting ⋮ Unnamed Item ⋮ Minimal surfaces in Euclidean spaces by way of complex analysis ⋮ Generic mean curvature flow. I: Generic singularities ⋮ Evolution of form and shape ⋮ Simulation of a Soap Film Möbius Strip Transformation ⋮ The space of embedded minimal surfaces of fixed genus in a 3-manifold. V. Fixed genus ⋮ Soap-film Möbius strip changes topology with a twist singularity ⋮ Positivity of the universal pairing in 3 dimensions ⋮ Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman ⋮ Helicoid-like minimal disks and uniqueness ⋮ Embedded minimal disks: Proper versus nonproper—global versus local ⋮ Shrinkwrapping and the taming of hyperbolic 3-manifolds ⋮ The classical theory of minimal surfaces ⋮ Curvature estimates for surfaces with bounded mean curvature ⋮ Non-simply connected minimal planar domains in $\mathbb {H}^2\times \mathbb {R}$

Cites Work

• Topology and curvature of minimal surfaces properly embedded in \(\mathbb{R}^ 3\)
• The strong halfspace theorem for minimal surfaces
• A complete minimal surface in \(R^ 3\) between two parallel planes
• 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
• Complete properly embedded minimal surfaces in \(\mathbf R^3\)
• The uniqueness of the helicoid
• The geometry of $G$-structures
• Hadamard's and Calabi-Yau's conjectures on negatively curved and minimal surfaces

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