Geometric Function Theory and Non-linear Analysis

Autor: Tadeusz Iwaniec, Gaven John Martin

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Editura: Oxford University Press

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This book provides a survey of recent developments in the field of non-linear analysis and the geome...

Informații despre carte

Autor

Tadeusz Iwaniec, Gaven John Martin

Limbă

engleză

Legare

Carte - Copertă tare

Publicat

2001

Pagini

568

EAN

9780198509295

ISBN

0198509294

Enbook ID

04526962

Editura

Oxford University Press

Greutate

1020

Dimensiuni

164 x 239 x 35

Descriere completă

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.

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