On the Koebe-Maskit theorem

Note on a Theorem of Bôcher and Koebe*

On the Shape of Bers–maskit Slices

We consider complex one-dimensional Bers–Maskit slices through the deformation space of quasifuchsian groups which uniformize a pair of punctured tori. In these slices, the pleating locus on one of the components of the convex hull boundary of the quotient three-manifold has constant rational pleating and constant hyperbolic length. We show that the boundary of such a slice is a Jordan curve wh...

1 5 N ov 2 00 6 ON KLEIN - MASKIT COMBINATION THEOREM IN SPACE I

In this paper, we generalise the first Klein-Maskit combination theorem to discrete groups of Möbius transformations in higher dimensions. As a simple application of the main theorem, some examples will be constructed.

Real C Koebe Principle

We prove a C version of the real Koebe principle for interval (or circle) maps with non-flat critical points.

Koebe 1/4-theorem and Inequalities in N=2 Super-qcd

The critical curve C on which Im τ̂ = 0, τ̂ = aD/a, determines hyperbolic domains whose Poincaré metric is constructed in terms of aD and a. We describe C in a parametric form related to a Schwarzian equation and prove new relations for N = 2 Super SU(2) Yang-Mills. In particular, using the Koebe 1/4-theorem and Schwarz’s lemma, we obtain inequalities involving u, aD and a, which seem related to ...