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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis
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Quasiregular Mappings (Paperback, Softcover reprint of the original 1st ed. 1993)
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Discovery Miles 20 740
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Quasiregular Mappings (Paperback, Softcover reprint of the original 1st ed. 1993)
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 26
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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.
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