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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 2, pp. 174–184, February, 2014.
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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 Math J 67, 199–210 (2015). https://doi.org/10.1007/s11253-015-1074-4
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DOI: https://doi.org/10.1007/s11253-015-1074-4