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.