We show that if G is a non-elementary torsion-free word hyperbolic group then there exists another word hyperbolic group G∗, such that G is a subgroup of G∗ but G is not quasiconvex in G∗ . We also prove that any non-elementary subgroup of a torsion-free word hyperbolic group G contains a free group of rank two which is malnormal and quasiconvex in G.

We generate a basis of the space of bicubic and biquartic C-smooth geometrically continuous isogeometric functions on bilinear multi-patch domains Ω ⊂ R. The basis functions are obtained by suitably combining C-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains (cf. [16]). They are described by simple explicit formulas for their spline coefficie...

The scaling function of a one-dimensional Markov map is defined and studied. We prove that the scaling function of a non-critical geometrically finite one-dimensional map is Hölder continuous, while the scaling function of a critical geometrically finite one-dimensional map is discontinuous. We prove that scaling functions determine Lipschitz conjugacy classes, and moreover, that the scaling fu...

In this paper, we prove some Hermite-Hadamard type inequalities for operator geometrically convex functions non-commutative operators.