Description
This book is about geometric function theory and nonlinear analysis. It surveys recent developments in the field, and discusses applications of the theory to various fields of mathematics.
A survey of recent developments in the field of non-linear analysis and the geometry of mappings. Sobolev mappings, quasiconformal mappings, or deformations, between subsets of Euclidean space, or manifolds or more general geometric objects may arise as the solutions to certain optimization problems in the calculus of variations or in non-linear elasticity, as the solutions to differential equations (particularly in conformal geometry), as local co-ordinates on a manifold or as geometric realizations of abstract isomorphisms between spaces such as those that arise in dynamical systems (for instance in holomorphic dynamics and Kleinian groups). In each case the regularity and geometric properties of these mappings and related non-linear quantities such as Jacobians, tells something about the problems and the spaces under consideration The applications studied include aspects of harmonic analysis, elliptic PDE theory, differential geometry, the calculus of variations as well as complex dynamics and other areas. Indeed it is the strong interactions between these areas and the geometry of mappings that underscores and motivates the authors' work. Review: This book makes life easier for all mathematicians interested in quasiconformal theory and all its generalisations, analysis of mappings between Euclidean spaces or manifolds, and all related areas ... The book is well written and may comfortably be read by advanced students. EMS The book begins with an expertly written overview, which will be of value even to specialists in the field ... authoritatively written by two of the leading figures in the field ... contains a wealth of material ... makes pleasant reading. Bulletin of the London Mathematical Society
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