Let X be a hyperbolic Riemann surface or orbifold, possibly of infinite topological complexity. Let φ : X → X be a quasiconformal map. We show the following conditions are equivalent (§1): (a) φ has… (More)

By applying the methods of V. Markovic [ 7] to the special case of Riemann surfaces of finite type, we obtain a transparent new proof of a classical result about isometries between the spaces of L 1… (More)

We use quasiconformal variations to study Riemann mappings onto variable single slit domains when the slit is the tail of an appropriately smooth Jordan arc. In the real analytic case our results… (More)

We extend Strebel’s theory of variability sets to the setting of arbitrary hyperbolic Riemann surfaces. Our extended theory depends on the behavior of the Teichmüller metric on the fibers of… (More)

According to a theorem of A. Grothendieck [4] the Teichmüller space of a closed Riemann surface of genus p ^ 2 is the universal parameter space for holomorphic families of marked Riemann surfaces of… (More)

We generalize a known inequality relating the Euclidean and hyperbolic metrics in Poincaré’s unit ball model of hyperbolic space. Our generalization applies to Schwarz-Pick metrics in the open unit… (More)

The Schottky space .9, of marked Schottky groups of genus p > 2 has very simple embeddings as a domain in C" , n : 3p 3, and is therefore a tempting place to study the Riemann space .R, of all closed… (More)