The Ubiquitous Quasidisk: (Mathematical Surveys and Monographs)

This book focuses on gathering the numerous properties and many different connections with various topics in geometric function theory that quasidisks possess. A quasidisk is the image of a disk under a quasiconformal mapping of the Riemann sphere. In 1981 Frederick W. Gehring gave a short course of six lectures on this topic in Montreal and his lecture notes ``Characteristic Properties of Quasidisks'' were published by the University Press of the University of Montreal. The notes became quite popular and within the next decade the number of characterizing properties of quasidisks and their ramifications increased tremendously. In the late 1990s Gehring and Hag decided to write an expanded version of the Montreal notes. At three times the size of the original notes, it turned into much more than just an extended version. New topics include two-sided criteria. The text will be a valuable resource for current and future researchers in various branches of analysis and geometry, and with its clear and elegant exposition the book can also serve as a text for a graduate course on selected topics in function theory. Frederick W. Gehring (1925-2012) was a leading figure in the theory of quasiconformal mappings for over fifty years. He received numerous awards and shared his passion for mathematics generously by mentoring twenty-nine Ph.D. students and more than forty postdoctoral fellows. Kari Hag received her Ph.D. under Gehring's direction in 1972 and worked with him on the present text for more than a decade.

Table of Contents:
Preface Part I. Properties of quasidisks Preliminaries Geometric properties Conformal invariants Injectivity criteria Criteria for extension Two-sided criteria Miscellaneous properties Part II. Some proofs of these properties First series of implications Second series of implications Third series of implications Fourth series of implications Bibliography Index

About the Author :
Frederick W. Gehring, Kari Hag, Norwegian University of Science and Technology, Trondheim, Norway

Review :
...This text on quasidisks provides a cross section of the plane quasiconformal theory and demonstrates the many ways in which these mappings are related to analysis, topology, geometry and other parts of mathematics. The exposition is very clear and the text is richly illustrated with carefully drawn pictures. This book would be an excellent choice for a first book on plane quasiconformal maps for a graduate student. It is also a valuable source of inspiration for researchers of complex analysis, because the material covers many topics of current interest. It is my guess that this book will be an instant classic in its field." - Matti Vuorinen (Turku), Zentralblatt MATH