On a conditional theorem of Littlewood for quasiregular entire functions (Q1326661)

As well-known, the theory of quasiregular maps in \(R^n\) uses a method from several mathematical disciplines such as Sobolev spaces, nonlinear PDE's, variational calculus, and potential theory. On the other hand, one of the main motivations for the theory is to generalize ``geometric'' properties of analytic functions of the plane. In the paper under review, these both aspects are apparent. The theorem in the title connects the multiplicity function and the order of an entire quasiregular mapping. The author makes skillfull use of highly technical estimates of generalized solutions of PDE's and also uses ideas from his earlier joint paper with A. Eremenko. It is noteworthy that some of the results are new even in the particular case of analytic functions.