TY - JOUR AU - A. L. Gol'berg AU - E. A. Sevost'yanov PY - 2015/02/25 Y2 - 2024/03/29 TI - On the Radius of Injectivity for Generalized Quasiisometries in the Spaces of Dimension Higher Than Two JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 67 IS - 2 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1972 AB - 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. ER -