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1
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Quasi-minimal rotational surfaces in pseudo-Euclidean four-dimensional space

100%
Ganchev G., Milousheva V.
Open Mathematics
|
2014
|
tom 12
|
nr 10
1586-1601
EN
In 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.
2
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Singularities of lightcone pedals of spacelike curves in Lorentz-Minkowski 3-space

100%
Chen L.
Open Mathematics
|
2016
|
tom 14
|
nr 1
889-896
EN
In this paper, geometric properties of spacelike curves on a timelike surface in Lorentz-Minkowski 3-space are investigated by applying the singularity theory of smooth functions from the contact viewpoint.
3
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Weighted minimal translation surfaces in the Galilean space with density

100%
Yoon D. W.
Open Mathematics
|
2017
|
tom 15
|
nr 1
459-466
EN
Translation surfaces in the Galilean 3-space G3 have two types according to the isotropic and non-isotropic plane curves. In this paper, we study a translation surface in G3 with a log-linear density and classify such a surface with vanishing weighted mean curvature.
4
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Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

100%
López R., Demir E.
Open Mathematics
|
2014
|
tom 12
|
nr 9
1349-1361
EN
We classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.
5
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Elastic Sturmian spirals in the Lorentz-Minkowski plane

76%
Uçum A., İlarslan K., Mladenov I. M.
Open Mathematics
|
2016
|
tom 14
|
nr 1
1149-1156
EN
In this paper we consider some elastic spacelike and timelike curves in the Lorentz-Minkowski plane and obtain the respective vectorial equations of their position vectors in explicit analytical form. We study in more details the generalized Sturmian spirals in the Lorentz-Minkowski plane which simultaneously are elastics in this space.
6
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Differential geometry of grassmannians and the Plücker map

76%
Anan’in S., Grossi C.
Open Mathematics
|
2012
|
tom 10
|
nr 3
873-884
EN
Using the Plücker map between grassmannians, we study basic aspects of classic grassmannian geometries. For ‘hyperbolic’ grassmannian geometries, we prove some facts (for instance, that the Plücker map is a minimal isometric embedding) that were previously known in the ‘elliptic’ case.
7
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Strengthened Moser’s conjecture, geometry of Grunsky coefficients and Fredholm eigenvalues

52%
Krushkal S.
Open Mathematics
|
2007
|
tom 5
|
nr 3
551-580
EN
The Grunsky and Teichmüller norms ϰ(f) and k(f) of a holomorphic univalent function f in a finitely connected domain D ∋ ∞ with quasiconformal extension to $$\widehat{\mathbb{C}}$$ are related by ϰ(f) ≤ k(f). In 1985, Jürgen Moser conjectured that any univalent function in the disk Δ* = {z: |z| > 1} can be approximated locally uniformly by functions with ϰ(f) < k(f). This conjecture has been recently proved by R. Kühnau and the author. In this paper, we prove that approximation is possible in a stronger sense, namely, in the norm on the space of Schwarzian derivatives. Applications of this result to Fredholm eigenvalues are given. We also solve the old Kühnau problem on an exact lower bound in the inverse inequality estimating k(f) by ϰ(f), and in the related Ahlfors inequality.
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