Related papers: Entire one-periodic maximal surfaces

We get a continuous one-parameter new family of embedded minimal surfaces, of which the period problems are two-dimensional. Moreover, one proves that it has Scherk second surface and Hoffman-Wohlgemuth example as limit-members.

We classify complete biharmonic surfaces with parallel mean curvature vector field and non-negative Gaussian curvature in complex space forms.

In this paper we study prime, maximal and two--class congruences from the point of view of the relationships between them in various kinds of universal algebras, as well as their direct and inverse images through morphisms. This research…

All families of sextic surfaces with the maximal number of isolated triple points are found.

A surface in the Teichm\"uller space, where the systole function attains its maximum, is called a maximal surface. For genus two there exists a unique maximal surface which is called the Bolza surface. In this article, we study the…

We classify and describe totally geodesic and parallel hypersurfaces for the entire class of Siklos spacetimes. A large class of minimal hypersurfaces is also described.

We study the tropical lines contained in smooth tropical surfaces in R^3. On smooth tropical quadric surfaces we find two one-dimensional families of tropical lines, like in classical algebraic geometry. Unlike the classical case, however,…

Harmonic mappings have long intrigued researchers due to their intrinsic connection with minimal surfaces. In this paper, we investigate shearing of two distinct classes of univalent conformal mappings which are convex in horizontal…

This paper develops new tools for understanding surfaces with more than one end (and usually, of infinite topology) which properly minimally embed into Euclidean three-space. On such a surface, the set of ends forms a compact Hausdorff…

We study the size and regularity properties of level sets of continuous functions with bounded upper-scaled and lower-scaled oscillation.

We classify hyperbolic polynomials in two real variables that admit a transitive action on some component of their hyperbolic level sets. Such surfaces are called special homogeneous surfaces, and they are equipped with a natural Riemannian…

A monoid hypersurface is an irreducible hypersurface of degree d which has a singular point of multiplicity d-1. Any monoid hypersurface admits a rational parameterization, hence is of potential interest in computer aided geometric design.…

We present a new family of embedded doubly periodic minimal surfaces, of which the symmetry group does not coincide with any other example known before.

The current paper discusses some new results about conformal polynomic surface parameterizations. A new theorem is proved: Given a conformal polynomic surface parameterization of any degree it must be harmonic on each component. As a first…

In this paper, we study tropicalisations of singular surfaces in toric threefolds. We completely classify singular tropical surfaces of maximal-dimensional type, show that they can generically have only finitely many singular points, and…

This paper investigates the global properties of a class of spherically symmetric spacetimes. The class contains the maximal development of asymptotically flat spherically symmetric initial data for a wide variety of coupled Einstein-matter…

Algebraic surfaces in the complex projective space with a high number of A-type singularities have been presented in a recent paper. We extend the construction in order to obtain lower bounds for the maximal number of A singularities for…

A classification of 2-dimensional surfaces imbedded in spacetime is presented, according to the algebraic properties of their shape tensor. The classification has five levels, and provides among other things a refinement of the concepts of…

Invariant minimal surfaces in the real special linear group of degree 2 with canonical Riemannian and Lorentzian metrics are studied. Constant mean curvature surfaces with vertically harmonic Gau{\ss} map are classified.

We study harmonic surfaces in $\mathbb{R}^3$ through the framework of harmonic Enneper immersions and prove a superposition principle for such surfaces. We prove that minimal and maximal surfaces admit a decomposition into harmonic…