Explore: Quasiconformal Mappings In Metric Spaces

eccentricity. Quasiconformal mappings are a generalization of conformal mappings that permit the bounded distortion of angles locally. Quasiconformal mappings were

the introduction of quasiconformal mappings to the subject. They allow us to give much more depth to the study of moduli spaces by endowing them with

In mathematics, a quasicircle is a Jordan curve in the complex plane that is the image of a circle under a quasiconformal mapping of the plane onto itself

it was the precursor of quasiconformal mappings and quadratic differentials, later developed as the technique of extremal metric due to Oswald Teichmüller

introduction of quasiconformal mappings and differential geometric methods into the study of Riemann surfaces. The Teichmüller space is named after him

include orientation-reversing mappings whose Jacobians can be written as any scalar times any orthogonal matrix. For mappings in two dimensions, the (orientation-preserving)

group Γ can be read off from such a polygon. Using the theory of quasiconformal mappings and the Beltrami equation, it can be shown there is a canonical

upper half plane and plays a fundamental role in Teichmüller theory and the theory of quasiconformal mappings. Various uniformization theorems can be proved

on quasiconformal mappings, Van Nostrand Ballmann, Werner; Gromov, Mikhael; Schroeder, Viktor (1985), Manifolds of nonpositive curvature, Progress in Mathematics

\xi ^{j}}}\right)=0,\qquad (g=\det\{g_{ij}\})} where gij is the Euclidean metric tensor relative to the new coordinates and Γ denotes its Christoffel symbols