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    GEOMETRIC FUNCTION THEORY AND NON-LINEAR ANALYSIS
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    501963

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    Sinopse

    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 variationsas 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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    ISBN9780198509295
    Peso634g
    Livro disponível - pronta entregaNão
    Tipo itemLivro Importado
    Número de páginas568
    Número da edição1ª EDIÇAO - 2001
    Código Interno501963
    Código de barras9780198509295
    AcabamentoHARDCOVER
    AutorIWANIEC, TADEUSZ | MARTIN, GAVEN
    EditoraOXFORD UK
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