Related papers: Entire one-periodic maximal surfaces
The purpose of this paper is to study complete $\lambda$-surfaces in Euclidean space $\mathbb R^3$. A complete classification for 2-dimensional complete $\lambda$-surfaces in Euclidean space $\mathbb R^3$ with constant squared norm of the…
We characterize helix surfaces (constant angle surfaces) in the special linear group $\mathrm{SL}(2,\r)$. In particular, we give an explicit local description of these surfaces in terms of a suitable curve and a 1-parameter family of…
We classify the space-like biharmonic surfaces in 3-dimension pseudo-Riemannian space form, and construct explicit examples of proper biharmonic hypersurfaces in general ADS space.
We introduce semi-helix hyper surfaces of Euclidean spaces. We also provide a local characterization of how these semi-helices are constructed.
We present dynamic equations for two dimensional closed surfaces and analytically solve it for some simplified cases. We derive final equations for surface normal motions by two different ways. The solution of the equations of motions in…
It is constructed a formal normal form, using an iterative normalization procedure, for a large class of Real-Smooth Hypersurfaces in Complex Spaces.
Biconservative surfaces are surfaces with divergence-free stress-bienergy tensor. Simply connected, complete, non-$CMC$ biconservative surfaces in $3$-dimensional space forms were constructed working in extrinsic and intrinsic ways. Then,…
Biharmonic hypersurfaces in a generic conformally flat space are studied in this paper. The equation of such hypersurfaces is derived and is used to determine the conformally flat metric $f^{-2}\delta_{ij}$ on the Euclidean space…
We present a notion of a random toric surface modeled on a notion of a random graph. We then study some threshold phenomena related to the smoothness of the resulting surfaces.
We study a global theory of affine maximal surfaces with singularities, which are called affine maximal maps and defined by Aledo--Mart\' inez--Mil\' an. In this paper, we define a special subclass of such surfaces other than improper…
We give a survey of results on the geometry of complex algebraic Q-acyclic surfaces, so-called 'Q-homology planes', including some recent results.
Let X be a closed oriented Riemann surface of genus > 1 of constant negative curvature -1. A surface containing a disk of maximal radius is an optimal surface. This paper gives exact formulae for the number of optimal surfaces of genus > 3…
We present two constructions, both inspired by ideas from graph theory, of sequences random surfaces of growing area, whose systoles grow logarithmically as a function of their area. This also allows us to prove a new lower bound on the…
We classify normal stable surfaces with $K_X^2 = 1$, $p_g = 2$ and $q=0$ with a unique singular point which is a non-canonical T-singularity, thus exhibiting two divisors in the main component and a new irreducible component of the moduli…
We construct examples of hyperbolic rational homology spheres and hyperbolic knot complements in rational homology spheres containing closed embedded totally geodesic surfaces.
Infinitesimal bendings for classes of two-dimensional surfaces in $\mathbb{R}^3$ are investigated. The techniques used to construct the bending fields include reduction to solvability of Bers-Vekua type equations and systems of differential…
Multilevel methods are among the most efficient numerical methods for solving large-scale systems of equations that arise from discretized partial differential equations. Two-level convergence theory plays a fundamental role in the analysis…
We show the existence of 1-parameter families of non-periodic, complete, embedded minimal surfaces in euclidean space with infinitely many parallel planar ends. In particular we are able to produce finite genus examples and quasi-periodic…
A geometrical correspondence between maximal surfaces in anti-De Sitter space-time and minimal surfaces in the Riemannian product of the hyperbolic plane and the real line is established. New examples of maximal surfaces in anti-De Sitter…
Compact locally maximal hyperbolic sets are studied via geometrically defined functional spaces that take advantage of the smoothness of the map in a neighborhood of the hyperbolic set. This provides a self-contained theory that not only…