Abstract
We study homeomorphisms of Riemannian manifolds with unbounded characteristic such that the inverse mappings satisfy the Poletsky-type inequality. It is established that their families are equicontinuous if the function Q which is related to the Poletsky inequality and is responsible for a distortion of the modulus, is integrable in the given domain, here the original manifold is connected and the domain of definition and the range of values of mappings have compact closures.
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 16, No. 4, pp. 557–566 October–December, 2019.
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Ilyutko, D.P., Sevost’yanov, E.A. On the Equicontinuity of Families of Inverse Mappings of Riemannian Manifolds. J Math Sci 246, 664–670 (2020). https://doi.org/10.1007/s10958-020-04771-8
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DOI: https://doi.org/10.1007/s10958-020-04771-8