The Apollonian metric: limits of the comparison and bilipschitz properties.
The Apollonian metric: uniformity and quasiconvexity.
The asymptotic behavior of Green's functions for quasi-hyperbolic metrics on degenerating Riemann surfaces.
The hyperbolic Carnot theorem in the Poincaré disc model of hyperbolic geometry.
The hyperbolic geometry of continued fractions .
The hyperbolic metric in a rectangle. II.
The hyperbolic metric of a rectangle.
The hyperbolic square and Möbius transformations.
The inner Carathédory distance for the annulus.
The Markovian hyperbolic triangulation
We construct and study the unique random tiling of the hyperbolic plane into ideal hyperbolic triangles (with the three corners located on the boundary) that is invariant (in law) with respect to Möbius transformations, and possesses a natural spatial Markov property that can be roughly described as the conditional independence of the two parts of the triangulation on the two sides of the edge of one of its triangles.
The Pick version of the Schwarz lemma and comparison of the Poincaré densities.
The quasihyperbolic metric, growth, and John domains.
The ratio of invariant metrics on the annulus and theta functions
The theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry
In [Comput. Math. Appl. 41 (2001), 135--147], A. A. Ungar employs the Möbius gyrovector spaces for the introduction of the hyperbolic trigonometry. This Ungar's work plays a major role in translating some theorems from Euclidean geometry to corresponding theorems in hyperbolic geometry. In this paper we explore the theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry.
Théorie de Voronoï géométrique. Propriétés de finitude pour les familles de réseaux et analogues
Nous développons une théorie de Voronoï géométrique. En l’appliquant aux familles classiques de réseaux euclidiens (par exemple symplectiques ou orthogonaux), nous obtenons notamment de nouveaux résultats de finitude concernant les configurations de vecteurs minimaux et les réseaux particuliers (par exemple parfaits) de ces familles. Les méthodes géométriques introduites sont également illustrées par l’étude d’objets voisins (formes de Humbert) ou analogues (surfaces de Riemann).
Two-point distortion theorems for bounded univalent functions.