Related papers: Entire one-periodic maximal surfaces
We establish the background for the study of geodesics on noncompact polygonal surfaces. For illustration, we study the recurrence of geodesics on $Z$-periodic polygonal surfaces. We prove, in particular, that almost all geodesics on a…
We classify $G$-solid rational surfaces over the field of complex numbers.
The zero level set of a piecewise-affine function with respect to a consistent tetrahedral subdivision of a domain in $\mathbb{R}^3$ is a piecewise-planar hyper-surface. We prove that if a family of consistent tetrahedral subdivions…
We consider harmonic immersions in $\R^{\N}$ of compact Riemann surfaces with finitely many punctures where the harmonic coordinate functions are given as real parts of meromorphic functions. We prove that such surfaces have finite total…
In this paper, we study geometry of totally real minimal surfaces in the complex hyperquadric $Q_{N-2}$, and obtain some characterizations of the harmonic sequence generated by these minimal immersions. For totally real flat surfaces that…
Surface waves supported by structured metallic surfaces, i.e. metasurfaces, have drawn wide attention recently. They are promising for various applications ranging from integrated photonic circuits to imaging and bio-sensing in various…
We describe the global dynamics of some pointwise periodic piecewise linear maps in the plane that exhibit interesting dynamic features. For each of these maps we find a first integral. For these integrals the set of values are discrete,…
An interesting problem in classical differential geometry is to find methods to prove that two surfaces defined by different charts actually coincide up to position in space. In a previous paper we proposed a method in this direction for…
Minimal surfaces with planar curvature lines in the Euclidean space have been studied since the late 19th century. On the other hand, the classification of maximal surfaces with planar curvature lines in the Lorentz-Minkowski space has only…
We give a complete topological classification of minimal surfaces in Euclidian three-space.
In this paper we introduce the notion of timelike surface with harmonic inverse mean curvature in 3-dimensional Lorentzian space forms, and study their fundamental properties.
We reconsider non-degenerate second order superintegrable systems in dimension two as geometric structures on conformal surfaces. This extends a formalism developed by the authors, initially introduced for (pseudo-)Riemannian manifolds of…
We investigate the logarithmic and power-type convexity of the length of the level curves for $a$-harmonic functions on smooth surfaces and related isoperimetric inequalities. In particular, our analysis covers the $p$-harmonic and the…
I present a new "Pairs of Squares" rendering of the Periodic Table. It takes advantage of the number of orbitals at each Madelung energy level being a whole square. This makes the table very uniform and intuitive in contrast with its…
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…
This article has two purposes. The first is to give an expository account of the integrable systems approach to harmonic maps from surfaces to Lie groups and symmetric spaces, focusing on spectral curves for harmonic 2-tori. The most…
We address the problem of when two finite dimensional central division algebras over the same field are necessarily isomorphic given that they have the same maximal subfields.
We study the degree growth of iterates of meromorphic selfmaps of compact Kahler surfaces. Using cohomology classes on the Riemann-Zariski space we show that the degrees grow similarly to those of mappings that are algebraically stable on…
We construct examples of flat surfaces in $\mathbb{H}^3$ which are graphs over a two-punctured horosphere and classify complete embedded flat surfaces in $\mathbb{H}^3$ with only one end and at most two isolated singularities.
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…