Not all Schottky groups of Möbius transformations are classical Schottky groups. In this paper we show that all Fuchsian Schottky groups are classical Schottky groups, but not necessarily on the same set of generators. AMS Classification 20H10; 30F35, 30F40

There are certain sequences of words in the generators of a twogenerator subgroup of SL(2,C) that frequently arise in the Teichmüller theory of hyperbolic three-manifolds and Kleinian groups. In this paper we establish the connection between two such families, the family of Farey words that have been used by Keen-Series to understand the boundaries of the Quasifuchsian space of surfaces of type...

We use rigid analytic uniformization by Schottky groups to give a bound for the order of the abelian subgroups of the automorphism group of a Mumford curve in terms of its genus.

We exhibit pairs of infinite-volume, hyperbolic three-manifolds that have the same scattering poles and conformally equivalent boundaries, but which are not isometric. The examples are constructed using Schottky groups and the Sunada construction. In memory of Evsey Dyn’kin

The Schottky barrier heights of metal contacts, including WSi0.8, Cr, Ti, Pt, and Ni, on n-type gallium nitride GaN with a GaN cap layer grown at low-temperature LTG were studied. Higher barriers can be formed by introducing LTG GaN on top of the conventional structures. The higher Schottky barrier observed in samples with the LTG GaN cap layer may be due to the facts that the high-resistivity ...

This note introduces and studies an open set of PSL2(C) characters of a nonabelian free group, on which the action of the outer automorphism group is properly discontinuous, and which is strictly larger than the set of discrete, faithful convex-cocompact (i.e. Schottky) characters. This implies, in particular, that the outer automorphism group does not act ergodically on the set of characters w...

Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal Schwarz Lemma and...

In this paper we look at a special type of discrete subgroups of PSLn+1(C) called Schottky groups. We develop some basic properties of these groups and their limit set when n > 1, and we prove that Schottky groups only occur in odd dimensions, i.e., they cannot be realized as subgroups of PSL2n+1(C).