On the order of growth of ring Q-homeomorphisms at infinity

Abstract

where M is the conformal modulus of a family of curves in R and K ≥ 1 is a certain constant. In other words, the modulus of any family of curves is distorted by at most a factor of K. Capacities and moduli form the basis of the main geometric method in the contemporary theory of mappings. In this connection, the following class of mappings was studied [2]: Let G be a domain in R , n ≥ 2, and let Q D : , → ∞ [ ] 1 be a measurable function. A homeomorphism f G n : → R = R ∪ ∞ { } is called a Q-homeomorphism if