We investigate the problem of extension of so-called ring Q-homeomorphisms between domains in metric spaces with measures to the boundary. We establish conditions for the function Q(x) and the boundary of the domain under which any ring Q-homeomorphism admits a continuous or a homeomorphic extension to the boundary. The results are applicable, in particular, to Riemannian manifolds, Löwner spaces, and Carnot and Heisenberg groups.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 5, pp. 682–689, May, 2010.
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Smolovaya, E.S. Boundary behavior of ring Q-homeomorphisms in metric spaces. Ukr Math J 62, 785–793 (2010). https://doi.org/10.1007/s11253-010-0388-5
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DOI: https://doi.org/10.1007/s11253-010-0388-5