The Phragmen-Lindelöf principle for quasiregular mappings of manifolds and the isoperimetry
The authors consider quasiregular mappings of a noncompact Riemannian manifold \(D\) in view of generalizations of the Phragmén-Lindelöf principle. Roughly speaking, the main result may be expressed as follows. Either the quasiregular mapping \(f\) grows rapidly in a certain sense or \(f\equiv\text{const}\) (Theorem 2). Finally, the authors give two applications of Theorem 2 to a quasiregular mapping \(f=(f_1,f_2, \dots, f_n): \mathbb{R}^n \supset D\to \mathbb{R}^n\) with \(f_1\leq 1\) on the boundary of \(D\), where \(D\) is a cone or a semicylinder, respectively. In this paper, the proofs are based on isoperimetry. This new approach allows the consideration of the Phragmén-Lindelöf principle for quasiregular mappings of manifolds.
scientific article; zbMATH DE number 1113092