On the Radius of Injectivity for Generalized Quasiisometries in the Spaces of Dimension Higher Than Two

Abstract

We consider a class of local homeomorphisms more general than the mappings with bounded distortion. Under these homeomorphisms, the growth of the p-module (n-1 < p ≤ n) of the families of curves is controlled by an integral containing an admissible metric and a measurable function Q. It is shown that, under generic conditions imposed on the majorant Q, this class has a positive radius of injectivity (and, hence, a ball in which every mapping is homeomorphic). Moreover, one of the conditions imposed on Q is not only sufficient but also necessary for existence of a radius of injectivity.