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

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.

Parametrization of a Family of Minimal Surfaces Bounded by the Broken Lines in

1997 ◽  
Vol 4 (3) ◽  
pp. 201-219
Author(s):  
R. Abdulaev
Keyword(s):  
Minimal Surfaces ◽  
Weierstrass Representation ◽  
Coordinate Plane ◽  
Parameter Domain

Abstract Consideration is given to a family of minimal surfaces bounded by the broken lines in which are locally injectively projected onto the coordinate plane. The considered family is bijectively mapped by means of the Enepper–Weierstrass representation onto a set of circular polygons of a certain type. The parametrization of this set is constructed, and the dimension of the parameter domain is established.

scholarly journals Minimal surfaces in 3-dimensional solvable Lie groups II

2006 ◽  
Vol 73 (3) ◽  
pp. 365-374 ◽  
Author(s):  
Jun-Ichi Inoguchi
Keyword(s):  
Integral Representation ◽  
Lie Groups ◽  
Minimal Surfaces ◽  
Representation Formula ◽  
Gauss Map ◽  
Invariant Metric ◽  
Solvable Lie Groups ◽  
3 Dimensional ◽  
Integral Representation Formula

An integral representation formula in terms of the normal Gauss map for minimal surfaces in 3-dimensional solvable Lie groups with left invariant metric is obtained.

scholarly journals Nambu-Goto Strings viaWeierstrass Representation

2017 ◽  
Vol 13 (4) ◽  
pp. 4985-4992
Author(s):  
Mahmoud Kotb
Keyword(s):  
Gauge Theory ◽  
Physical Properties ◽  
Minimal Surface ◽  
Minimal Surfaces ◽  
String Model ◽  
Gauss Curvature ◽  
Weierstrass Representation ◽  
Perturbative Solution ◽  
Goto Action

A description of string model of gauge theory are related to minimal surfaces. notations of minimal surface and related mean and Gauss curvature discussed. The Weierstrass representation for a surface conformally which immersed in R used to represent Nambu- Goto action, action of Nambu Goto is calculated usingWeierstrass representation which can be used to calculate the Partion Function and potential, then a non-perturbative solution for action is aimed and fulfilled and a consequences of that are investigated and its mathematical and physical properties are discussed.

scholarly journals A generalized Weierstrass representation of Lorentzian surfaces in ℝ2,2 and applications

2016 ◽  
Vol 13 (06) ◽  
pp. 1650074 ◽  
Author(s):  
Victor Patty
Keyword(s):  
Dimensional Space ◽  
Representation Formula ◽  
De Sitter Space ◽  
Weierstrass Representation ◽  
Spinor Representation ◽  
De Sitter ◽  
Lorentzian Surface ◽  
Lorentz Surface

We give a generalized Weierstrass formula for a Lorentz surface conformally immersed in the four-dimensional space [Formula: see text] using spinors and Lorentz numbers. We also study the immersions of a Lorentzian surface in the Anti-de Sitter space (a pseudo-sphere in [Formula: see text]): we give a new spinor representation formula and deduce the conformal description of a flat Lorentzian surface in that space.

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