Surgeries on small volume hyperbolic 3-orbifolds.
Symmetries of Riemann Surfaces with Large Automorphism Group.
Systole et invariant d'Hermite.
Systole growth for finite area hyperbolic surfaces
In this note, we observe that the maximum value achieved by the systole function over all complete finite area hyperbolic surfaces of a given signature is greater than a function that grows logarithmically in terms of the ratio .
Systoles of arithmetic surfaces and the Markoff spectrum.
Systoles on Riemann surfaces.
Tameness on the boundary and Ahlfors' measure conjecture
Let N be a complete hyperbolic 3-manifold that is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We show N is homeomorphic to the interior of a compact 3-manifold, or tame, if one of the following conditions holds: 1. N has non-empty conformal boundary, 2. N is not homotopy equivalent to a compression body, or 3. N is a strong limit of geometrically finite manifolds. The first case proves Ahlfors’ measure conjecture for kleinian groups in the closure of the geometrically finite...
Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards.
Teichmüller space is not Gromov hyperbolic.
Teichmüller spaces and BMOA.
Teichmüller spaces are not starlike.
Teichmüller spaces with variable bases in the universal Teichmüller space.
Teichmüller theory of bordered surfaces.
Teichmüllerraum für total degenerierte Kurven.
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 bounded model for hyperbolic 3-space and a quaternionic uniformization theorem.
The box-counting dimension for geometrically finite Kleinian groups
We calculate the box-counting dimension of the limit set of a general geometrically finite Kleinian group. Using the 'global measure formula' for the Patterson measure and using an estimate on the horoball counting function we show that the Hausdorff dimension of the limit set is equal to both: the box-counting dimension and packing dimension of the limit set. Thus, by a result of Sullivan, we conclude that for a geometrically finite group these three different types of dimension coincide with the...
The chordal norm of discrete Möbius groups in several dimensions.