The weierstrass representation and the classical examples

1986 ◽  
pp. 10-27
Author(s):  
J. Lucas M. Barbosa ◽  
A. Gervasio Colares
Keyword(s):  
Weierstrass Representation

Description of a 3-periodic minimal surface family with trigonal symmetry

1994 ◽  
Vol 209 (1) ◽  
Author(s):  
A. Fogden
Keyword(s):  
Minimal Surface ◽  
Minimal Surfaces ◽  
Weierstrass Representation ◽  
Systematic Analysis ◽  
Trigonal Symmetry ◽  
Triply Periodic Minimal Surfaces ◽  
Periodic Minimal Surface ◽  
Triply Periodic ◽  
The Family

AbstractA systematic analysis of a family of triply periodic minimal surfaces of genus seven and trigonal symmetry is given. The family is found to contain five such surfaces free from self-intersections, three of which are previously unknown. Exact parametrisations of all surfaces are provided using the Weierstrass representation.

A Weierstrass Representation for Minimal Surfaces in 3-Dimensional Manifolds

2011 ◽  
Vol 60 (1-4) ◽  
pp. 311-323 ◽  
Author(s):  
J. H. Lira ◽  
M. Melo ◽  
F. Mercuri
Keyword(s):  
Minimal Surfaces ◽  
Weierstrass Representation ◽  
3 Dimensional

scholarly journals The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1

2008 ◽  
Vol 80 (1) ◽  
pp. 3-19
Author(s):  
Shuguo Shi
Keyword(s):  
Nonlinear Equation ◽  
Representation Formula ◽  
Gauss Map ◽  
Weierstrass Representation ◽  
Fully Nonlinear ◽  
Duality Property ◽  
Fully Nonlinear Equation ◽  
Monge Ampere

In this paper, we introduce the fourth fundamental forms for hypersurfaces in Hn+1 and space-like hypersurfaces in S1n+1, and discuss the conformality of the normal Gauss map of the hypersurfaces in Hn+1 and S1n+1. Particularly, we discuss the surfaces with conformal normal Gauss map in H³ and S³1, and prove a duality property. We give a Weierstrass representation formula for space-like surfaces in S³1 with conformal normal Gauss map. We also state the similar results for time-like surfaces in S³1. Some examples of surfaces in S³1 with conformal normal Gauss map are given and a fully nonlinear equation of Monge-Ampère type for the graphs in S³1 with conformal normal Gauss map is derived.

scholarly journals C∞-Convergence of Circle Patterns to Minimal Surfaces

2009 ◽  
Vol 194 ◽  
pp. 149-167 ◽  
Author(s):  
Shi-Yi Lan ◽  
Dao-Qing Dai
Keyword(s):  
Minimal Surface ◽  
Existence Theorem ◽  
Minimal Surfaces ◽  
Weierstrass Representation ◽  
Circle Pattern ◽  
Vertex Set ◽  
Circle Patterns ◽  
Simply Connected Region ◽  
Simply Connected ◽  
The Relationship

AbstractGiven a smooth minimal surface F: Ω → ℝ3 defined on a simply connected region Ω in the complex plane ℂ, there is a regular SG circle pattern . By the Weierstrass representation of F and the existence theorem of SG circle patterns, there exists an associated SG circle pattern in ℂ with the combinatoric of . Based on the relationship between the circle pattern and the corresponding discrete minimal surface F∊: → ℝ3 defined on the vertex set of the graph of , we show that there exists a family of discrete minimal surface Γ∊: → ℝ3, which converges in C∞(Ω) to the minimal surface F: Ω → ℝ3 as ∊ → 0.

A Weierstrass Representation Formula for Minimal Surfaces in ℍ3 and ℍ2 × ℝ

2005 ◽  
Vol 22 (6) ◽  
pp. 1603-1612 ◽  
Author(s):  
Francesco Mercuri ◽  
Stefano Montaldo ◽  
Paola Piu
Keyword(s):  
Minimal Surfaces ◽  
Representation Formula ◽  
Weierstrass Representation
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