On the Radius of Injectivity for Generalized Quasiisometries in the Spaces of Dimension Higher Than Two
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.
English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 2, pp 199-210.
Citation Example: Gol'berg A. L., Sevost'yanov E. A. On the Radius of Injectivity for Generalized Quasiisometries in the Spaces of Dimension Higher Than Two // Ukr. Mat. Zh. - 2015. - 67, № 2. - pp. 174-184.