Chebyshev polynomials and inequalities for Kleinian groups

Iteration Theory and Inequalities for Kleinian Groups

Chebyshev Polynomials and Markov–bernstein Type Inequalities for Rational Spaces

This paper considers the trigonometric rational system

Mating Kleinian Groups Isomorphic to C2 ∗ C5 with Quadratic Polynomials

Given a quadratic polynomial q : Ĉ→ Ĉ and a representation G : Ĉ→ Ĉ of C2 ∗C5 in PSL(2,C) satisfying certain conditions, we will construct a 4 : 4 holomorphic correspondence on the sphere (given by a polynomial relation p(z,w)) that mates the two actions: The sphere will be partitioned into two completely invariant sets Ω and Λ. The set Λ consists of the disjoint union of two sets, Λ+ and Λ−, e...

Commensurability riteria for Kleinian groups

Bounded Geometry for Kleinian Groups

We show that a Kleinian surface group, or hyperbolic 3manifold with a cusp-preserving homotopy-equivalence to a surface, has bounded geometry if and only if there is an upper bound on an associated collection of coefficients that depend only on its end invariants. Bounded geometry is a positive lower bound on the lengths of closed geodesics. When the surface is a once-punctured torus, the coeff...