On the Isomorphism Theorem for Kleinian Groups.
On the Margulis constant for Kleinian groups. I.
On the scalar curvature of self-dual manifolds.
On the shape of Bers-Maskit slices.
On uniqueness of automorphisms groups of Riemann surfaces.
OPTi's algorithm for discreteness determination.
Polynomial complexity of the Gilman-Maskit discreteness algorithm.
Quasiconformal groups of compact type.
We establish that a quasiconformal group is of compact type if and only if its limits set is purely conical and find that the limit set of a quasiconformal group of compact type is uniformly perfect. A key tool is the result of Bowditch-Tukia on compact-type convergence groups. These results provide crucial tools for studying the deformations of quasiconformal groups and in establishing isomorphisms between such groups and conformal groups.
Quasiregular semigroups.
Reduced Bers boundaries of Teichmüller spaces
We consider a quotient space of the Bers boundary of Teichmüller space, which we call the reduced Bers boundary, by collapsing each quasi-conformal deformation space lying there into a point.This boundary turns out to be independent of the basepoint, and the action of the mapping class group extends continuously to this boundary.This is an affirmative answer to Thurston’s conjecture.He also conjectured that this boundary is homeomorphic to the unmeasured lamination space by the correspondence coming...
Regular and limit sets for holomorphic correspondences
Holomorphic correspondences are multivalued maps between Riemann surfaces Z and W, where Q̃₋ and Q̃₊ are (single-valued) holomorphic maps from another Riemann surface X onto Z and W respectively. When Z = W one can iterate f forwards, backwards or globally (allowing arbitrarily many changes of direction from forwards to backwards and vice versa). Iterated holomorphic correspondences on the Riemann sphere display many of the features of the dynamics of Kleinian groups and rational maps, of which...
Remarks on points of approximation of discrete sugroups of U(1,n; C).
Rigidity and inflexibility in conformal dynamics.
Rigidity of cusps in deformations of hyperbolic 3-orbifolds.
Schottky uniformizations of Z22 actions on Riemann surfaces.
Given a closed Riemann surface S together a group of its conformal automorphisms H ≅ Z22, it is known that there are Schottky uniformizations of S realizing H. In this note we proceed to give an explicit Schottky uniformizations for each of all different topological actions of Z22 as group of conformal automorphisms on a closed Riemann surface.
Sector estimates for Kleinian groups.
Sector reflections in the plane.
Self-embeddings of kleinian groups
Simultaneous uniformisation.
Singular sets of holonomy maps for algebraic foliations
In this article we investigate the natural domain of definition of a holonomy map associated to a singular holomorphic foliation of the complex projective plane. We prove that germs of holonomy between algebraic curves can have large sets of singularities for the analytic continuation. In the Riccati context we provide examples with natural boundary and maximal sets of singularities. In the generic case we provide examples having at least a Cantor set of singularities and even a nonempty open set...