Publication list for Martin, Gaven

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
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    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
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    Online Price 2: 92.80
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    Print Add to Cart URL: /some/url/at/AMS/SURV-216
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    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 Beltrami Equation
    Base Product Code Keyword List: memo; MEMO; memo/191; MEMO/191; memo-191; MEMO-191; memo/191/893; MEMO/191/893; memo-191-893; MEMO-191-893
    Print Product Code: MEMO/191/893
    Online Product Code: MEMO/191/893.E
    Title (HTML): The Beltrami Equation
    Author(s) (Product display): Tadeusz Iwaniec; Gaven Martin
    Affiliation(s) (HTML): Syracuse University, Syracuse, NY; Massey University, Albany, Auckland, New Zealand
    Abstract:

    The “measurable Riemann Mapping Theorem” (or the existence theorem for quasiconformal mappings) has found a central rôle in a diverse variety of areas such as holomorphic dynamics, Teichmüller theory, low dimensional topology and geometry, and the planar theory of PDEs. Anticipating the needs of future researchers, the authors give an account of the “state of the art” as it pertains to this theorem, that is, to the existence and uniqueness theory of the planar Beltrami equation, and various properties of the solutions to this equation. The classical theory concerns itself with the uniformly elliptic case (quasiconformal mappings). Here the authors develop the theory in the more general framework of mappings of finite distortion and the associated degenerate elliptic equations.

    The authors recount aspects of this classical theory for the uninitiated, and then develop the more general theory. Much of this is either new at the time of writing, or provides a new approach and new insights into the theory. Indeed, it is the substantial recent advances in non-linear harmonic analysis, Sobolev theory and geometric function theory that motivated their approach here. The concept of a principal solution and its fundamental role in understanding the natural domain of definition of a given Beltrami operator is emphasized in their investigations. The authors believe their results shed considerable new light on the theory of planar quasiconformal mappings and have the potential for wide applications, some of which they discuss.

    Book Series Name: Memoirs of the American Mathematical Society
    Publication Month and Year: 2008-01-15
    Copyright Year: 2008
    Page Count: 92
    Cover Type: Softcover
    Print ISBN-13: 978-0-8218-4045-0
    Online ISBN 13: 978-1-4704-0499-4
    Print ISSN: 0065-9266
    Online ISSN: 0065-9266
    Primary MSC: 35
    Textbook?: False
    Applied Math?: False
    Electronic Media?: False
    Apparel or Gift: False
    SXG Subject: DE
    Online Price 1 Label: List
    Online Price 1: 68.00
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    Review Copy: http://www.ams.org/exam-desk-review-request?&eisbn=978-1-4704-0499-4&pisbn=978-0-8218-4045-0&epc=MEMO/191/893.E&ppc=MEMO/191/893&title=The%20Beltrami%20Equation&author=Tadeusz%20Iwaniec%3B%20Gaven%20Martin&type=R