Nikola Lakic

Quasiconformal Teichmüller theory

Quasiconformal mapping Riemann surfaces Quadratic differentials, Part I Quadratic differentials, Part II Teichmuller equivalence The Bers embedding Kobayashis metric on Teichmuller space Isomorphisms and automorphisms Teichmuller uniqueness The mapping class group Jenkins-Strebel differentials Measured foliations Obstacle problems Asymptotic Teichmuller space Asymptotically extremal maps Universal Teichmuller space Substantial boundary points Earthquake mappings Bibliography Index.

Comparing Poincare densities

However, there is no formula for the Poincare density pn of a general plane domain Q, and so one must resort to estimates. Many research articles have been devoted to finding and working with such estimates (see for example [4], [5], [15], [19], [24], and [25]). The first tool to establish such estimates is Schwarzs lemma which says that every holomorphic map is a contraction with respect to the Poincare metric. That is, ps(f)ldf I< pD(z)Idzl, for any holomorphic map f from a Riemann surface D to another Riemann surface Q. Applying this lemma

Smale’s mean value conjecture and the coefficients of univalent functions

We study Smales mean value conjecture and its connection with the second coefficients of univalent functions. We improve the bound on Smales constant given by Beardon, Minda and Ng.

A hyperelliptic realization of the horseshoe and baker maps

We present a generalization of the functional equation for the Weierstrassk

A Vector Field Approach to Mapping Class Actions

wp

Tracking a moving point in the plane

-function for hyperelliptic surfaces of infinite genus arising from iteration of the horseshoe and baker maps. The ramified cover of these infinite genus surfaces over the complex plane are associated to a quadratic differential of finite norm with simple poles accumulating to infinity. We study the geometry of its critical trajectories emanating from these poles and their rate of accumulation.

The mapping class group

We present a vector field method for showing that certain subgroups of the mapping class group

Quasiconformal Teichm? uller Theory

Gamma

Asymptotic Teichmüller space

of a Riemann surface of infinite topological type act properly discontinuously. We apply the method to the group of homotopy classes of quasiconformal self-maps of the complement

VARIABILITY SETS ON RIEMANN SURFACES AND FORGETFUL MAPS BETWEEN TEICHM ˜ ULLER SPACES

Omega