Minimal surfaces in euclidean 3-space and their mean curvature 1 cousins in hyperbolic 3-space

DOI10.1590/S0001-37652003000300002zbMath1056.53038MaRDI QIDQ4456562

Shoichi Fujimori

Publication date: 16 March 2004

Published in: Anais da Academia Brasileira de Ciências (Search for Journal in Brave)

zbMATH Keywords

minimal surfaces in Euclidean spaceconstant mean curvature surfaces in hyperbolic space

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (1)

Spacelike surfaces in \(\mathbb{L}^4\) with null mean curvature vector and the nonlinear Riccati partial differential equation

Cites Work

• A rigidity theorem for properly embedded minimal surfaces in \(R^ 3\)
• The topology of complete minimal surfaces of finite total Gaussian curvature
• Uniqueness, symmetry, and embeddedness of minimal surfaces
• On complete minimal surfaces whose Gauss map misses two directions
• Irreducible constant mean curvature 1 surfaces in hyperbolic space with positive genus
• Complete surfaces of constant mean curvature-1 in the hyperbolic 3-space
• The geometry of finite topology Bryant surfaces
• Complete minimal surfaces in \(S^ 3\)
• A parametrization of the Weierstrass formulae and perturbation of complete minimal surfaces in R3 into the hyperbolic 3-space.
• The Classification of Complete Minimal Surfaces with Total Curvature Greater Than -12&#960
• The number of faces in a minimal foam
• Surfaces of constant mean curvature one in the hyperbolic three-space with irregular ends
• On the geometry of constant mean curvature one surfaces in hyperbolic space

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