Boundary behavior of ring Q-homeomorphisms in metric spaces
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.
English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 5, pp 785-793.
Citation Example: Smolovaya E. S. Boundary behavior of ring Q-homeomorphisms in metric spaces // Ukr. Mat. Zh. - 2010. - 62, № 5. - pp. 682–689.