Chirurgie croisée
Déformation J-équivalente de polynômes géometriquement finis
Any geometrically finite polynomial f of degree d ≥ 2 with connected Julia set is accessible by structurally stable sub-hyperbolic polynomials of the same degree. Moreover, they are topologically conjugate to f on their Julia sets.
Déformation localisée de surfaces de Riemann.
Let Y be a Riemann surface with compact boundary embedded into a hyperbolic Riemann surface of finite type X. It is proved that the space of deformations D of Y into X is an open subset of the Teichmüller space T(X) of X. Furthermore, D has compact closure if and only if Y is simply connected or isomorphic to a punctured disk, and D= T(X) if and only if the components of X Y are all disks or punctured disks.
Empilements de cercles et modules combinatoires
Le but de cette note est de tenter d’expliquer les liens étroits qui unissent la théorie des empilements de cercles et des modules combinatoires et de comparer les approches à la conjecture de J.W. Cannon qui en découlent.
Convergence of pinching deformations and matings of geometrically finite polynomials
We give a thorough study of Cui's control of distortion technique in the analysis of convergence of simple pinching deformations, and extend his result from geometrically finite rational maps to some subset of geometrically infinite maps. We then combine this with mating techniques for pairs of polynomials to establish existence and continuity results for matings of polynomials with parabolic points. Consequently, if two hyperbolic quadratic polynomials tend to their respective root polynomials...
Harmonic measures versus quasiconformal measures for hyperbolic groups
We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green metric, a metric which provides a geometric point of view on random walks and, in particular, which allows us to interpret harmonic measures as quasiconformal measures on the boundary of the group.
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