EMS Tracts in Mathematics 2013; 214 pp; hardcover Volume: 19 ISBN10: 3037191228 ISBN13: 9783037191224 List Price: US$78 Member Price: US$62.40 Order Code: EMSTM/19
 This book is intended for researchers interested in new aspects of local behavior of plane mappings and their applications. The presentation is selfcontained, but the reader is assumed to know basic complex and real analysis. The study of the local and boundary behavior of quasiconformal and biLipschitz mappings in the plane forms the core of the book. The concept of the infinitesimal space is used to investigate the behavior of a mapping at points without differentiability. This concept, based on compactness properties, is applied to regularity problems of quasiconformal mappings and quasiconformal curves, boundary behavior, weak and asymptotic conformality, local winding properties, variation of quasiconformal mappings, and criteria of univalence. Quasiconformal and biLipschitz mappings are instrumental for understanding elasticity, control theory and tomography, and the book also offers a new look at the classical areas such as the boundary regularity of a conformal map. Complicated local behavior is illustrated by many examples. The text offers a detailed development of the background for graduate students and researchers. Starting with the classical methods to study quasiconformal mappings, this treatment advances to the concept of the infinitesimal space and then relates it to other regularity properties of mappings in Part II. The new unexpected connections between quasiconformal and biLipschitz mappings are treated in Part III. There is an extensive bibliography. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Researchers interested in new aspects of local behavior of plane mappings and their applications. Table of Contents I. Quasiconformal Mappings in the Plane  Background of the theory
 Conformal invariants
 Definitions of quasiconformal maps
 Compactness and convergence theory
 Beltrami differential equation
II. Infinitesimal Geometry of Quasiconformal Maps  Infinitesimal space
 Asymptotically conformal curves
 Conformal differentiability
 Points of maximal stretching
 Lipschitz continuity of quasiconformal maps
 Regularity of quasiconformal curves
 Regularity of conformal maps at the boundary
III. Applications of Quasiconformal Maps  John's rotation problem
 Variation of quasiconformal maps
 Criteria of univalence
 Bibliography
 Index
