Quasiregular Mappings
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Beschreibung
Quasiregular Mappings extend quasiconformal theory to the
noninjective case.They give a natural and beautiful
generalization of the geometric aspects ofthe theory of
analytic functions of one complex variable to Euclidean
n-space or, more generally, to Riemannian n-manifolds. This
book is a self-contained exposition of the subject. A braod
spectrum of results of both analytic and geometric character
are presented, and the methods vary accordingly. The main
tools are the variational integral method and the extremal
length method, both of which are thoroughly developed here.
Reshetnyak's basic theorem on discreteness and openness is
used from the beginning, but the proof by means of
variational integrals is postponed until near the end. Thus,
the method of extremal length is being used at an early
stage and leads, among other things, to geometric proofs of
Picard-type theorems and a defect relation, which are some
of the high points of the present book.
This book is an introduction to the theory of quasiregular mappings in real n-dimensional space, a new field of mathematical study that has emerged during the past 20 years. The exposition is self-contained and thus accessible to a wide readership. A broad spectrum of results of both analytic and geometric character are presented, and the methods vary accordingly. The main tools are the variational integral method and the extremal length method, both of which are thoroughly developed here. The author is noted as one of the developers of the theory of quasiregular mappings, particularly for his work in value distribution theory. Many of the topics treated here are published for the first time in book form.
Autor*in
Seppo Rickman
Themen in »Quasiregular Mappings«
Extremal Length Extremale Länge Länge Nichtlineare Potentialtheorie Nonlinear Potential Theory Potential theory Quasiconformal Mappings Quasikonforme Abbildungen Quasiregular Mappings Quasiregulare Abbildungen Value Distribution Wertverteilung character conformal map manifold