Counting immersed surfaces in hyperbolic 3-manifolds.
Counting rooted trees: the universal law .
Counting walks in a quadrant: a unified approach via boundary value problems
The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this yields for the first time an explicit expression of the counting generating function. Moreover, the nature of the integrand of the integral formulations is shown to be directly dependent on the finiteness of a naturally attached group of birational transformations...
Courbes de Jordan vérifiant une condition corde-arc
Soit une courbe de Jordan fermée rectifiable dans le plan de la variable complexe. On dit que véfifie la condition corde-arc sioù est la longueur du plus petit arc de joignant et . Soit une représentation conforme du disque unité dans l’intérieur de . Nous prouvons que restreint à appartient à la classe de Muckenhoupt et nous en tirons certains corollaires. Dans deux cas particuliers nous montrons que le résultat peut être amélioré.
Covering of radial segments for domains bounded by -circles.
Covering properties of meromorphic functions, negative curvature and spherical geometry.
Covering spaces of families of compact Riemann surfaces.
Covering Theorems for Univalent Functions.
Critère de rationalité
Critère de reconnaissabilité de fonctions analytiques et fonctions entières arithmétiques
Criteria for (sub-)harmonicity and continuation of (sub-)harmonic functions.
Criteria for univalence of certain integral operators.
Criteria for univalence, starlikeness and convexity
Let 𝓐 denote the class of all normalized analytic functions f (f(0) = 0 = f'(0)-1) in the open unit disc Δ. For 0 < λ ≤ 1, define 𝓤(λ) = {f ∈ 𝓐 : |(z/f(z))²f'(z) - 1| < λ, z ∈ Δ} and 𝓟(2λ) = f ∈ 𝓐 : |(z/f(z))''| < 2λ, z ∈ Δ.cr Recently, the problem of finding the starlikeness of these classes has been considered by Obradović and Ponnusamy, and later by Obradović et al. In this paper, the authors consider the problem of finding the order...
Criterion of the reality of zeros in a polynomial sequence satisfying a three-term recurrence relation
This paper establishes the necessary and sufficient conditions for the reality of all the zeros in a polynomial sequence generated by a three-term recurrence relation with the standard initial conditions where and are arbitrary real polynomials.
Croissance de certaines séries de Dirichlet et applications.
Croissance des solutions d'une équation différentielle homogène
Croissance et meilleure approximation polynomiale des fonctions entieres
Cross ratios, Anosov representations and the energy functional on Teichmüller space
We study two classes of linear representations of a surface group: Hitchin and maximal symplectic representations. We relate them to cross ratios and thus deduce that they are displacing which means that their translation lengths are roughly controlled by the translations lengths on the Cayley graph. As a consequence, we show that the mapping class group acts properly on the space of representations and that the energy functional associated to such a representation is proper. This implies the existence...
Cross ratios, surface groups, and diffeomorphisms of the circle
This article relates representations of surface groups to cross ratios. We first identify a connected component of the space of representations into PSL(n,ℝ) – known as the n-Hitchin component– to a subset of the set of cross ratios on the boundary at infinity of the group. Similarly, we study some representations into associated to cross ratios and exhibit a “character variety” of these representations. We show that this character variety contains alln-Hitchin components as well as the set of...
Curvature and Functions with Bounded Boundary Rotation.