The ubiquitous quasidisk / Frederick W. Gehring, Kari Hag ; with contributions by Ole Jacob Broch.

Format:

Book

Author/Creator:

Gehring, Frederick W., author.

Hag, Kari, 1941- author.

Contributor:

Broch, Ole Jacob, contributor.

Series:

Mathematical surveys and monographs ; Volume 184.

Mathematical surveys and monographs ; Volume 184

Language:

English

Subjects (All):

Quasiconformal mappings.

Geometric function theory.

Functions of a complex variable.

Physical Description:

1 online resource (xi, 171 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2012]

Language Note:

English

Summary:

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.

Contents:

Cover

Title page

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

Back Cover.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (pages 163-168) and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

0-8218-9409-9

OCLC:

898200432