About a decade ago Thurston proved that a vast collection of 3-manifolds carry metrics of
constant negative curvature. These manifolds are thus elements of {\em hyperbolic …

This course will concern the interaction between:• hyperbolic geometry in dimensions 2 and
3;• the dynamics of iterated rational maps; and• the theory of Riemann surfaces and their …

In a striking pair of papers, McMullen gave a new proof of the contraction properties of
Thurston's “skinning map”–an iteration on the Teichmüller space of a Riemann surface. His …

Let π: Y→ X be a covering map between complex manifolds X and Y. For many holomorphic
objects (such as functions or forms) one can define a pushforward operator π∗ carrying …

We discuss universal properties of general Teichmüller spaces. Our topics include the
Teichmüller metric and Kobayashi metric, extremality and unique extremality of …

Let Σ be a hyperbolic Riemann surface, with a covering map π: Δ→ Σ, where Δ is the unit
disc. Let Λ be a closed subset of Σ such that π− 1 (Σ− Λ) is connected. Let k≥ 2 be an …

The 8 problem addressed by this theorem arises in in several of our previous papers. It is
connected w for multiple-valued holomorphic functions (see [Dil] a about solving the 8 …

We show that given a multiply-connected domain Ω with a holomorphic, multiple-valued
function F whose values are bounded on compact subsets of Ω, one cannot always find a …

On a problem of Seiberg and Witten Page 1 ANNALES POLONICI MATHEMATICI LXX (1998)
On a problem of Seiberg and Witten by David E. Barrett (Ann Arbor, Mich.) Abstract. We describe …

We explore the use of Levi-flat surfaces with circular cross-sections to study bounded
holomorphic functions on domains in C. Our first chapter records various characterizations of …