Two-dimensional minimal surfaces in a pseudo-Euclidean space

1991 ◽  
Vol 54 (1) ◽  
pp. 691-699 ◽  
Author(s):  
V. P. Gorokh
Keyword(s):  
Euclidean Space ◽  
Minimal Surfaces ◽  
Two Dimensional

scholarly journals Quasi-minimal rotational surfaces in pseudo-Euclidean four-dimensional space

2014 ◽  
Vol 12 (10) ◽  
Author(s):  
Georgi Ganchev ◽  
Velichka Milousheva
Keyword(s):  
Vector Field ◽  
Euclidean Space ◽  
Minimal Surfaces ◽  
Mean Curvature ◽  
Dimensional Space ◽  
Curvature Vector ◽  
Parabolic Type ◽  
Mean Curvature Vector ◽  
Two Dimensional ◽  
Rotational Surfaces

AbstractIn the four-dimensional pseudo-Euclidean space with neutral metric there are three types of rotational surfaces with two-dimensional axis — rotational surfaces of elliptic, hyperbolic or parabolic type. A surface whose mean curvature vector field is lightlike is said to be quasi-minimal. In this paper we classify all rotational quasi-minimal surfaces of elliptic, hyperbolic and parabolic type, respectively.

scholarly journals Unification and classification of two-dimensional crystalline patterns using orbifolds

2014 ◽  
Vol 70 (4) ◽  
pp. 319-337 ◽  
Author(s):  
S. T. Hyde ◽  
S. J. Ramsden ◽  
V. Robins
Keyword(s):  
Euclidean Space ◽  
Minimal Surfaces ◽  
Three Dimensional ◽  
Hyperbolic Groups ◽  
Dimensional Euclidean Space ◽  
Two Dimensional ◽  
Triply Periodic Minimal Surfaces ◽  
Triply Periodic ◽  
Simple Rules

The concept of an orbifold is particularly suited to classification and enumeration of crystalline groups in the euclidean (flat) plane and its elliptic and hyperbolic counterparts. Using Conway's orbifold naming scheme, this article explicates conventional point, frieze and plane groups, and describes the advantages of the orbifold approach, which relies on simple rules for calculating the orbifold topology. The article proposes a simple taxonomy of orbifolds into seven classes, distinguished by their underlying topological connectedness, boundedness and orientability. Simpler `crystallographic hyperbolic groups' are listed, namely groups that result from hyperbolic sponge-like sections through three-dimensional euclidean space related to all known genus-three triply periodic minimal surfaces (i.e.theP,D,Gyroid,CLPandHsurfaces) as well as the genus-fourI-WPsurface.

An asymptotic analysis for Hamilton–Jacobi equations with large Hamiltonian drift terms

2017 ◽  
Vol 0 (0) ◽  
Author(s):  
Taiga Kumagai
Keyword(s):  
Asymptotic Behavior ◽  
Euclidean Space ◽  
Asymptotic Analysis ◽  
Open Subset ◽  
Dimensional Euclidean Space ◽  
Asymptotic Behavior Of Solutions ◽  
Two Dimensional ◽  
Jacobi Equations ◽  
Drift Terms

AbstractWe investigate the asymptotic behavior of solutions of Hamilton–Jacobi equations with large Hamiltonian drift terms in an open subset of the two-dimensional Euclidean space. The drift is given by

ON EUCLIDEAN G-MANIFOLDS WHICH HAVE TWO DIMENSIONAL ORBIT SPACES

2011 ◽  
Vol 22 (03) ◽  
pp. 399-406
Author(s):  
R. MIRZAIE
Keyword(s):  
Euclidean Space ◽  
Half Plane ◽  
Lie Group ◽  
Orbit Space ◽  
Two Dimensional ◽  
Orbit Spaces ◽  
Group Of Isometries ◽  
Connected Lie Group

We show that the orbit space of Euclidean space, under the action of a closed and connected Lie group of isometries is homeomorphic to a plane or closed half-plane, if the action is of cohomogeneity two.

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