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The 'measurable Riemann Mapping Theorem' has found a central role in a diverse variety of areas such as holomorphic dynamics, Teichmuller theory, low dimensional topology and geometry, and the planar theory of PDEs. The authors recount aspects of this clas

This book offers a modern, up-to-date introduction to quasiconformal mappings from an explicitly geometric perspective, emphasizing both the extensive developments in mapping theory during the past few decades and the remarkable applications of geometric function theory to other fields, including dynamical systems, Kleinian groups, geometric topology, differential geometry, and geometric group theory. It is a careful and detailed introduction to the higher-dimensional theory of quasiconformal mappings from the geometric viewpoint, based primarily on the technique of the conformal modulus of a...