Related papers: Penner coordinates for closed surfaces
This article is a survey article that gives detailed constructions and illustrations of some of the standard examples of non-orientable surfaces that are embedded and immersed in 4-dimensional space. The illustrations depend upon their…
We construct and classify, in the case of two complex dimensions, the possible tangent cones at points of limit spaces of non-collapsed sequences of K\"ahler-Einstein metrics with cone singularities.
We consider triangulations of closed $2$-dimensional (not necessarily orientable) surfaces. Any minimal set of zigzags that double covers the set of edges provides a $z$-orientation of the triangulation. We introduce Markov chains of…
For two closed curves on a plane (discrete version) and local criteria for similarity of points on the curves one gets a potential, which describes the similarity between curve points. This is the base for a global similarity measure of…
In this paper, we introduce a new asymmetric weak metric on the Teichm{\"u}ller space of a closed orientable surface with (possibly empty) punctures.This new metric, which we call the Teichm{\"u}ller-Randers metric, is an asymmetric…
In this paper we give some coupled fixed point results for mappings satisfying different contractive conditions on complete partial metric spaces.
Localization properties for Schr\"odinger means are studied in dimension higher than one.
This paper considers generalizations of open mappings, closed mappings, pseudo-open mappings, and quotient mappings from topological spaces to generalized topological spaces. Characterizations of these classes of mappings are obtained and…
A countable dense set of directions is sufficient for Steiner symmetrization, but the order of directions matters.
In the Kerr geometry, we calculate various surfaces of constant curvature invariants. These extend well beyond the Kerr horizon, and we argue that they might be of observational significance in connection with non-minimally coupled matter…
Finite element codes typically use data structures that represent unstructured meshes as collections of cells, faces, and edges, each of which require associated coordinate systems. One then needs to store how the coordinate system of each…
The unit vectors transformation between the Cartesian and the novel Similar Oblate Spheroidal coordinates, and vice versa, is derived. It can help to transform vector fields between these two types of orthogonal coordinates which can…
Those maps of a closed surface to the three-dimensional torus that are homotopic to embeddings are characterized. Particular attention is paid to the somewhat intricate case when the surface is nonorientable.
We construct compact arbitrary Euler characteristic orientable and non-orientable minimal surfaces in the Berger spheres. Besides we show an interesting family of surfaces that are minimal in every Berger sphere, characterizing them by this…
Infinite graphs are finitary in the sense that their points are connected via finite paths. So what would an infinitary generalization of finite graphs look like? Usually this question is answered with the aid of topology, e.g. in the case…
We study collections of curves in generic position on a closed surface whose complement consists of one disk only, up to orientation-preserving homeomorphism of the surface. We define a surgery operation on the set of such collections and…
The $\lambda$-perfect maps, a generalization of perfect maps (continuous closed maps with compact fibers) are presented. Using $P_\lambda$-spaces and the concept of $\lambda$-compactness some results regarding $\lambda$-perfect maps will be…
By using a certain second order differential equation, the notion of adapted coordinates on Finsler manifolds is defined and some classifications of complete Finsler manifolds are found. Some examples of Finsler metrics, with positive…
We study Bott-Chern cohomology on compact complex non-K\"ahler surfaces. In particular, we compute such a cohomology for compact complex surfaces in class $\text{VII}$ and for compact complex surfaces diffeomorphic to solvmanifolds.
We consider circle patterns on surfaces with complex projective structures. We investigate two symplectic forms pulled back to the deformation space of circle patterns. The first one is Goldman's symplectic form on the space of complex…