Related papers: Certain Constant Angle Surfaces Constructed on Cur…
We characterize Salem numbers which have some power arising as dynamical degree of an automorphism on a complex (projective) 2-Torus, K3 or Enriques surface.
We prove that the Cox ring of a smooth rational surface with big anticanonical class is finitely generated. We classify surfaces of this type that are blow-ups of the plane at distinct points lying on a (possibly reducible) cubic.
We consider conformal metrics of constant curvature 1 on a Riemann surface, with finitely many prescribed conic singularities and prescribed angles at these singularities. Especially interesting case which was studied by C. L. Chai, C. S…
We survey some results on real rational surfaces focused on their topology and their birational geometry.
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This last one classifies the case of $a^3b$-quadrilaterals with some irrational angle: there are a sequence of…
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 discuss K3 surfaces in characteristic two that contain the Kummer configuration formed by smooth rational curves on it.
We study parallel surfaces and dual surfaces of cuspidal edges. We give concrete forms of principal curvature and principal direction for cuspidal edges. Moreover, we define ridge points for cuspidal edges by using those. We clarify…
It is formally constructed a normal form for a class of real-formal surfaces defined near a CR Singularity.
We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of…
This study defines finite-type invariants for curves on surfaces and reveals the construction of these finite-type invariants for stable homeomorphism classes of curves on compact oriented surfaces without boundaries. These invariants are a…
In this paper, using the classifications of timelike and spacelike ruled surfaces, we study the Mannheim offsets of timelike ruled surfaces in Minkowski 3-space. Firstly, we define the Mannheim offsets of a timelike ruled surface by…
We characterize the representations of the fundamental group of a closed surface to $\mathrm{PSL}_2(\mathbb C)$ that arise as the holonomy of a branched complex projective structure with fixed branch divisor. In particular, we compute the…
This paper examines the relationship between the knotting of an embedded surface in $\R^3$ and the knotting of its fold curves, formed by the singular set of projection to a plane. The first result shows that every surface, no matter how…
We study in this work flat surfaces with conical singularities, that is, surfaces provided with a flat structure with conical singular points. Finding good parameters for these surfaces in the general case is an open question. We give an…
We show the existence of several new families of non-compact constant mean curvature surfaces: (i) singly-punctured surfaces of arbitrary genus $g \geq 1$, (ii) doubly-punctured tori, and (iii) doubly periodic surfaces with Delaunay ends.
Surfaces with concentric $K$-contours and parallel $K$-contours in Euclidean $3$-space are defined. Crucial examples are presented and characterization of them are given.
We present a discrete theory for modeling developable surfaces as quadrilateral meshes satisfying simple angle constraints. The basis of our model is a lesser known characterization of developable surfaces as manifolds that can be…
Let M be the interior of a compact 3-manifold with non-empty boundary, and T be an ideal (topological) triangulation of M. This paper describes necessary and sufficient conditions for the existence of angle structures, semi-angle structures…
In this paper, based on the theory of surfaces in the four-dimensional Euclidean space which generalizes the theory of surfaces in three-dimensional Euclidean space, beside other results, we will give a characterization of points on…