Publication list for Gehring, Frederick

Latest Titles

  • An Introduction to the Theory of Higher-Dimensional Quasiconformal Mappings
    Base Product Code Keyword List: surv; SURV; surv/216; SURV/216; surv-216; SURV-216
    Print Product Code: SURV/216
    Online Product Code: SURV/216.E
    Title (HTML): An Introduction to the Theory of Higher-Dimensional Quasiconformal Mappings
    Author(s) (Product display): Frederick W. Gehring; Gaven J. Martin; Bruce P. Palka
    Affiliation(s) (HTML): Massey University, Auckland, New Zealand; National Science Foundation, Arlington, VA
    Abstract:

    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 curve family. Notably, the final chapter describes the application of quasiconformal mapping theory to Mostow's celebrated rigidity theorem in its original context with all the necessary background.

    This book will be suitable as a textbook for graduate students and researchers interested in beginning to work on mapping theory problems or learning the basics of the geometric approach to quasiconformal mappings. Only a basic background in multidimensional real analysis is assumed.

    Book Series Name: Mathematical Surveys and Monographs
    Volume: 216
    Publication Month and Year: 2017-05-03
    Copyright Year: 2017
    Page Count: 430
    Cover Type: Hardcover
    Print ISBN-13: 978-0-8218-4360-4
    Online ISBN 13: 978-1-4704-4046-6
    Print ISSN: 0076-5376
    Online ISSN: 0076-5376
    Primary MSC: 30
    Textbook?: false
    Applied Math?: false
    Home Page?: false
    Sample?: false
    Reference?: false
    Electronic Media?: false
    Apparel or Gift: false
    SXG Subject: AN
    Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/surv-216
    Online Price 1 Label: List
    Online Price 1: 116.00
    Print Price 1 Label: List
    Print Price 1: 116.00
    Online Price 2 Label: Individual Member
    Online Price 2: 92.80
    Print Price 2 Label: Individual Member
    Print Price 2: 92.80
    Dual Price 1 Label: List
    Dual Price 1: 145
    Dual Price 2 Label: Individual Member
    Dual Price 2: 116
    Print Outstock Reason: TOS
    Print Outstock Reason Avail Date: Expected availability date October 12, 2017
    Print Add to Cart URL: /some/url/at/AMS/SURV-216
    Electronic Add to Cart URL: /some/url/at/AMS/SURV-216.E
    Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-4046-6&pisbn=978-0-8218-4360-4&epc=SURV/216.E&ppc=SURV/216&title=An%20Introduction%20to%20the%20Theory%20of%20Higher-Dimensional%20Quasiconformal%20Mappings&author=Frederick%20W.%20Gehring%3B%20Gaven%20J.%20Martin%3B%20Bruce%20P.%20Palka&type=R
    Readership:

    Graduate students and researchers interested in mapping theory.

    Related Products: Lectures on Quasiconformal Mappings The Ubiquitous Quasidisk
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  • The Ubiquitous Quasidisk
    Base Product Code Keyword List: surv; SURV; surv/184; SURV/184; surv-184; SURV-184
    Print Product Code: SURV/184
    Online Product Code: SURV/184.E
    Title (HTML): The Ubiquitous Quasidisk
    Author(s) (Product display): Frederick W. Gehring; Kari Hag
    Affiliation(s) (HTML): Norwegian University of Science and Technology, Trondheim, Norway
    Abstract:

    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.

    Book Series Name: Mathematical Surveys and Monographs
    Volume: 184
    Publication Month and Year: 2012-11-08
    Copyright Year: 2012
    Page Count: 171
    Cover Type: Hardcover
    Print ISBN-13: 978-0-8218-9086-8
    Online ISBN 13: 978-0-8218-9409-5
    Print ISSN: 0076-5376
    Online ISSN: 0076-5376
    Primary MSC: 30
    Textbook?: False
    Applied Math?: False
    Electronic Media?: False
    Apparel or Gift: False
    SXG Subject: AN
    Supplemental Materials (URL at AMS): http://www.ams.org/bookpages/surv-184
    Online Price 1 Label: List
    Online Price 1: 74.00
    Print Price 1 Label: List
    Print Price 1: 74.00
    Online Price 2 Label: Individual Member
    Online Price 2: 59.20
    Print Price 2 Label: Individual Member
    Print Price 2: 59.20
    Print Add to Cart URL: /some/url/at/AMS/SURV-184
    Electronic Add to Cart URL: /some/url/at/AMS/SURV-184.E
    Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-0-8218-9409-5&pisbn=978-0-8218-9086-8&epc=SURV/184.E&ppc=SURV/184&title=The%20Ubiquitous%20Quasidisk&author=Frederick%20W.%20Gehring%3B%20Kari%20Hag&type=R
    Readership:

    Graduate students and research mathematicians interested in geometric function theory.

    Reviews:

    ...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

    Related Products: Lectures on Quasiconformal Mappings Quasiformal Mappings