Related papers: Characterizing the Delaunay decompositions of comp…
The situation of the decay of the metastable phase on the several types of heterogeneous centers is described analytically. The total number of heterogeneous centers is supposed to be equal for different types. This description decomposes…
In this paper we describe trigonometry on the de Sitter surface. For that a characterization of geodesics is given, leading to various types of triangles. We define lengths and angles of these. Then, transferring the concept of polar…
Convex co-compact 3-dimensional hyperbolic manifolds are uniquely determined by the pleating measured lamination on the boundary of their convex core.
We present a general methodology for electromagnetic homogenization and characterization of bianisotropic metasurfaces formed by regular or random arrangements of small arbitrary inclusions at the interface of two different isotropic media.…
We construct minimal surfaces in hyperbolic and anti-de Sitter 3-space with the topology of a $n$-punctured sphere by loop group factorization methods. The end behavior of the surfaces is based on the asymptotics of Delaunay-type surfaces,…
A main result in this paper is the proof that proximal Delaunay triangulation regions are convex polygons. In addition, it is proved that every Delaunay triangulation region has a local Leader uniform topology.
We prove that any compact surface with constant positive curvature and conical singularities can be decomposed into irreducible components of standard shape, glued along geodesic arcs connecting conical singularities. This is a spherical…
In a previous work arXiv:physics/0611108v2, it was shown that the volume spanned by a molecular system in its conformational space can be effectively bounded by a polyhedral cone, this cone is described by means of a simple combinatorial…
We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of…
We consider a discrete dynamical system on a pseudo-Riemannian manifold and we determine the concept of a hyperbolic set for it. We insert a condition in the definition of a hyperbolic set which implies to the unique decomposition of a part…
We compare the flat geometry associated to a quadratic differential with the hyperbolic geometry associated to the underlying Riemann surface. We show that if a curve is contained in a thick subsurface, then its hyperbolic length is…
Global and local regularities of functions are analyzed in anisotropic function spaces, under a common framework, that of hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities…
Given a pair of points in the hyperbolic half plane or the unit disk, we provide a simple construction of the midpoint of the hyperbolic geodesic segment joining the points.
We show that any surface admits an area preserving $C^{1+\beta}$ diffeomorphism with non-zero Lyapunov exponents which is Bernoulli and has polynomial decay of correlations. We establish both upper and lower polynomial bounds on…
We prove that a cyclic cover of a smooth complex projective variety is Brody hyperbolic if its branch divisor is a generic small deformation of a large enough multiple of a Brody hyperbolic base-point-free ample divisor. We also show the…
Delaunay triangulations of a point set in the Euclidean plane are ubiquitous in a number of computational sciences, including computational geometry. Delaunay triangulations are not well defined as soon as 4 or more points are concyclic but…
The JSJ decomposition encodes the automorphisms and the virtually cyclic splittings of a hyperbolic group. For general finitely presented groups, the JSJ decomposition encodes only their splittings. In this sequence of papers we study the…
We develop a theory for distributed branch points and investigate their role in determining the shape and influencing the mechanics of thin hyperbolic objects. We show that branch points are the natural topological defects in hyperbolic…
A planar set $P$ is said to be cover-decomposable if there is a constant $k=k(P)$ such that every $k$-fold covering of the plane with translates of $P$ can be decomposed into two coverings. It is known that open convex polygons are…
Consider the Poincare disc model for hyperbolic geometry. In this paper, a convenient computational formula is developed along with an aesthetic geometric interpretation. Two proofs, one geometric and one analytical, of each result are…