Complete properly embedded minimal surfaces in \(\mathbf R^3\)

DOI10.1215/S0012-7094-01-10726-6zbMath1010.49025OpenAlexW2068983621MaRDI QIDQ1847824

Tobias Holck Colding, William P. II. Minicozzi

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-01-10726-6

zbMATH Keywords

finite total curvatureminimal surfacesminimal annulus

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (7)

A note on an overdetermined problem for minimal surface equation ⋮ Evolution of form and shape ⋮ Shapes of embedded minimal surfaces ⋮ The space of embedded minimal surfaces of fixed genus in a 3-manifold. V. Fixed genus ⋮ Some Picard theorems for minimal surfaces ⋮ The classical theory of minimal surfaces ⋮ On properly embedded minimal surfaces with three ends.

Cites Work

• Topology and curvature of minimal surfaces properly embedded in \(\mathbb{R}^ 3\)
• Doubly-connected minimal surfaces
• The geometry and conformal structure of properly embedded minimal surfaces of finite topology in \(\mathbb{R}^ 3\)
• Differential equations on riemannian manifolds and their geometric applications
• Convergence of embedded minimal surfaces without area bounds in three-manifolds
• The Asymptotic Behavior of Properly Embedded Minimal Surfaces of Finite Topology
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