General univalence criteria in the disk: Extensions and extremal function.
Generalized John disks
We establish the basic properties of the class of generalized simply connected John domains.
Geometric characterization for affine mappings and Teichmüller mappings
We characterize affine mappings on the unit disk and on rectangles by module conditions. The main result generalizes the classic Schwarz lemma. As an application, we give a sufficient condition for a K-quasiconformal mapping on a Riemann surface to be a Teichmüller mapping.
Geometric characterization for homeomorphisms between disks
We give some characterizations for certain homeomorphisms between disks in the complex plane, and we prove some Schwarz type theorems for such homeomorphisms. Our results replace the main result of Chen [Studia Math. 157 (2003)] which we show to be false.
Geometric properties of solutions to the anisotropic -Laplace equation in dimension two.
Growth of the coefficient auf quasiconformality and the boundary correspondence of automorphisms of a ball.
Grunsky coefficient inequalities, Caratheodory metric and extremal quasiconformal mappings.