Travaux de Thurston sur les groupes quasi-fuchsiens et les variétés hyperboliques de dimension fibrées sur
The theory of slice-regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains of . When is a symmetric slice domain, the twistor transform of such a function is a holomorphic curve in the Klein quadric. The case in which is the complement of a parabola is studied in detail and described by a rational quartic surface in the twistor space .
Doubling measures appear in relation to quasiconformal mappings of the unit disk of the complex plane onto itself. Each such map determines a homeomorphism of the unit circle on itself, and the problem arises, which mappings f can occur as boundary mappings?
We study the relationship between linear isoperimetric inequalities and the existence of non-constant positive harmonic functions on Riemann surfaces.We also study the relationship between growth conditions of length of spheres and the existence and the existence of Green's function on Riemann surfaces.
The topology of the maximal-ideal space of is discussed.