Basic Properties of Quasiregular Mappings
We shall define quasiregular mappings analytically following Yu.G. Reshetnyak. At an early stage we take full advantage of Reshetnyak’s important discovery 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 ACLP mappings contains fairly standard preliminary results. Discrete open mappings are considered in Section 4 as a separate topic, mostly without proofs. The material of the first chapter is primarily concerned with various aspects of the definition of quasiregularity.
KeywordsNormal Domain Local Degree Weak Partial Derivative Quasiregular Mapping Normal Neighborhood
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