Titlebook: Quasiregular Mappings; Seppo Rickman Book 1993 Springer-Verlag Berlin Heidelberg 1993 Extremal Length.Extremale L?nge.L?nge.Nichtlineare P

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Basic Properties of Quasiregular Mappings,overy that a nonconstant quasiregular mapping is discrete and open, but put off the proof to Chapter VI. This way we are able to have a coherent geometric treatment without introducing an excessive amount of machinery at the outset. Section 1 on ACL. mappings contains fairly standard preliminary res

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Applications of Modulus Inequalities,ions will be given in Chapters IV, V, and VII. We start with some global distortion results and continue by proving, among other things, that a nonconstant qr mapping of ?. into itself omits at most a set of zero capacity. A local form of the latter result will be used in the proof of a Picard-type

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Variational Integrals and Quasiregular Mappings, qr mappings as counterparts for harmonic functions in the plane. Nonlinearity enters in the theory for dimensions . ≥ 3: the Euler—Lagrange equations for such variational integrals are not linear, but only quasilinear partial differential equations. For that reason methods familiar from the classic

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Boundary Behavior,the early stage of the development of the theory some of these counterparts were established by O. Martio and S. Rickman [MR1]. Later M. Vuorinen continued this line of research in a number of articles, see 2.3 and 7.4. The tool in [MR1] and mostly in Vuorinen’s articles is the method of extremal le

Bernstein-test

Mappings into the ,-Sphere with Punctures,the article [R11]. In Section 3 we will give a quantitative growth estimate for mappings of the unit ball into the .-sphere with punctures, which delivers as a special case a counterpart to the Picard-Schottky theorem of classical function theory.

闡釋

Variational Integrals and Quasiregular Mappings, for such variational integrals are not linear, but only quasilinear partial differential equations. For that reason methods familiar from the classical theory are for the most part not applicable to this nonlinear potential theory.

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0071-1136 aspects ofthe theory ofanalytic functions of one complex variable to Euclideann-space or, more generally, to Riemannian n-manifolds.Thisbook is a self-contained exposition of the subject. Abraodspectrum of results of both analytic and geometric characterarepresented, and the methods vary accordingly