Related papers: Une sextique hyperbolique dans P^3(C)

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.

We study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface can have (the so-called kissing number for hyperbolic…

We present a basic introduction to the theories of M\"obius structures and hyperbolic ends and we study their applications to the theory of $k$-surfaces in $3$-dimensional hyperbolic space.

We classify Coxeter decompositions of hyperbolic tetrahedra, i.e. simplices in the hyperbolic space H^3. The paper completes the classification of Coxeter decompositions of hyperbolic simplices.

Generalizing both hyperbolic framed surfaces and one-parameter families of hyperbolic framed curves, we introduce the concept of hyperbolic generalized framed surfaces and establish their relations in hyperbolic 3-space. We provide the…

In this note we derive a new Minkowski-type inequality for closed convex surfaces in the hyperbolic 3-space. The inequality is obtained by explicitly computing the area of the family of surfaces obtained from the normal flow and then…

We study parabolic linear Weingarten surfaces in hyperbolic space $\rlopezh^3$. In particular, we classify two family of parabolic surfaces: surfaces with constant Gaussian curvature and surfaces that satisfy the relation…

We prove that the maximal number of conics in a smooth sextic $K3$-surface $X\subset\mathbb{P}^4$ is 285, whereas the maximal number of real conics in a real sextic is 261. In both extremal configurations, all conics are irreducible.

We show that every closed, virtually fibered hyperbolic 3-manifold contains immersed, quasi-Fuchsian surfaces with convex cores of arbitrarily large thickness.

We propose a Lie geometric point of view on flat fronts in hyperbolic space as special omega-surfaces and discuss the Lie geometric deformation of flat fronts.

We develop a simple procedure that allows one to explicitly reconstruct any piecewise linear path from its signature. The construction is based on the development of the path onto the hyperbolic space.

This is the third in a series of papers constructing hyperbolic structures on all Haken three-manifolds. This portion deals with the mixed case of the deformation space for manifolds with incompressible boundary that are not acylindrical,…

It is given a topological pinching for the injectivity radius of a compact embedded surface either in the sphere or in the hyperbolic space

There are three complete plane geometries of constant curvature: spherical, Euclidean and hyperbolic geometry. We explain how a closed oriented surface can carry a geometry which locally looks like one of these. Focussing on the hyperbolic…

We consider strong symplectic fillings of the unit cotangent bundle of a hyperbolic surface, equipped with its canonical contact structure. We show that every finitely presentable group can be realised as the fundamental group of such a…

Let M be a closed hyperbolic three manifold. We construct closed surfaces which map by immersions into M so that for each one the corresponding mapping on the universal covering spaces is an embedding, or, in other words, the corresponding…

We show that all hyperbolic surfaces admit an ideal triangulation with bounded shear parameters. This upper bound depends logarithmically on the topology of the surface.

By taking quotients of a certain tiling of hyperbolic plane / space by certain group actions, we obtain geometric polyhedra / cellulations with interesting symmetries and incidence structure.

We classify all real hypersurfaces with three distinct constant principal curvatures in complex hyperbolic spaces of dimension greater than two.

We introduce semi-helix hyper surfaces of Euclidean spaces. We also provide a local characterization of how these semi-helices are constructed.