Geometric Function Theory and Non-linear Analysis [Hardcover]

Tadeusz Iwaniec (Author), Gaven Martin (Author)

Book Description

Publication Date: January 15, 2002 | ISBN-10: 0198509294 | ISBN-13: 978-0198509295 | Edition: 1st

This book provides a survey of recent developments in the field of non-linear analysis and the geometry of mappings. Sobolev mappings, quasiconformal mappings, or deformations, between subsets of Euclidean space, or manifolds or more general geometric objects may arise as the solutions to certain optimisation problems in the calculus of variations or in non-linear elasticity, as the solutions to differential equations (particularly in conformal geometry), as local co-ordinates on a manifold or as geometric realisations of abstract isomorphisms between spaces such as those that arise in dynamical systems (for instance in holomorphic dynamics and Kleinian groups). In each case the regularity and geometric properties of these mappings and related non-linear quantities such as Jacobians, tells something about the problems and the spaces under consideration. The applications studied include aspects of harmonic analysis, elliptic PDE theory, differential geometry, the calculus of variations as well as complex dynamics and other areas. Indeed it is the strong interactions between these areas and the geometry of mappings that underscores and motivates the authors' work. Much recent work is included. Even in the classical setting of the Beltrami equation or measurable Riemann mapping theorem, which plays a central role in holomorphic dynamics, Teichmuller theory and low dimensional topology and geometry, the authors present precise results in the degenerate elliptic setting. The governing equations of non-linear elasticity and quasiconformal geometry are studied intensively in the degenerate elliptic setting, and there are suggestions for potential applications for researchers in other areas.

Editorial Reviews

Review

"Every reader interested in the modern viewpoint of geometric function theory will find a wide range of appealing topics in this book. It is particularly useful to see how some highly sohisticated machinery of real and harmonic analysis is developed and employed. This book will become a standard reference for the field."--Mathematical Reviews

About the Author

Tadeusz Iwaniec is a John Raymond French Distinguished Professor of Mathematics at Syracuse University. Gaven John Martin is a Professor of Mathematics and James Cook Fellow of Royal Society, New Zealand.

Product Details

• Hardcover: 568 pages
• Publisher: Oxford University Press, USA; 1st edition (January 15, 2002)
• Language: English
• ISBN-10: 0198509294
• ISBN-13: 978-0198509295
• Product Dimensions: 9.3 x 6.4 x 1.3 inches
• Shipping Weight: 2 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #3,974,843 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.