On the Convergence of Mappings in Metric Spaces with Direct and Inverse Modulus Conditions

T. Adamowicz and N. Shanmugalingam, “Non-conformal Loewner type estimates for modulus of curve families,” Ann. Acad. Sci. Fenn. Math., 35, 609–626 (2010).

V. Gutlyanskii, V. Ryazanov, and E. Yakubov, “The Beltrami equations and prime ends,” J. Math. Sci., 210, No. 1, 22–51 (2015).

P. Hajlasz and P. Koskela, “Sobolev met Poincare,” Mem. Amer. Math. Soc., 145, No. 688, 1–101 (2000).

J. Heinonen, Lectures on Analysis on Metric Spaces, Springer, New York (2001).

J. Onninen and K. Rajala, “Quasiregular mappings to generalized manifolds,” J. Anal. Math., 109, 33–79 (2009).

V. I. Ryazanov and R. R. Salimov, “Weakly flat spaces and boundaries in the theory of mappings,” Ukr. Mat. Vestn., 4, No. 2 199–234 (2007).

S. Rickman, Quasiregular Mappings, Springer, Berlin (1993).

O. Martio, V. Ryazanov, U. Srebro, and E. Yakubov, Moduli in Modern Mapping Theory, Springer, New York (2009).

J. Väisälä, Lectures on n-Dimensional Quasiconformal Mappings, Springer, Berlin (1971).

O. Martio, S. Rickman, and J. V¨ais¨al¨a, “Definitions for quasiregular mappings,” Ann. Acad. Sci. Fenn., Ser. A1. Math., 448, 1–40 (1969)

W. Hurewicz and H. Wallman, Dimension Theory, Princeton Univ. Press, Princeton (1948).

E. A. Sevost'yanov, "On the openness and discreteness of mappings with unbounded characteristic of quasiconformality," Ukr. Mat. Zh., 63, No. 8, 1128-1134 (2011)

English translation: Ukr. Math. J., 63, No. 8, 1298-1305 (2012).

E. A. Sevost’yanov, “On the lightness of the limit of a sequence of generalized-quasiconformal mappings,” Mat. Zametki, 102, No. 4, 586–596 (2017).

B. Fuglede, “Extremal length and functional completion,” Acta Math., 98, 171–219 (1957).

E. A. Sevost’yanov, “On the equicontinuity of homeomorphisms with unbounded characteristic,” Mat. Tr., 15, No. 1, 178–204 (2012).

E. S. Smolovaya, "Boundary behavior of ring Q-homeomorphisms in metric spaces," Ukr. Mat. Zh., 62, No. 5, 682-689 (2010)

English translation: Ukr. Math. J., 62, No. 5, 785-793 (2010).

J. Herron and P. Koskela, “Quasiextremal distance domains and conformal mappings onto circle domains,” Complex Var. Theor. Appl., 15, 167–179 (1990).

K. Kuratowski, Topology, Vol. 2, Academic Press, New York (1968).

R. Näkki and B. Palka, “Uniform equicontinuity of quasiconformal mappings,” Proc. Amer. Math. Soc., 37, No. 2, 427–433 (1973).

L. V. Keldysh, “Topological embeddings in Euclidean spaces,” Tr. Mat. Inst. Akad. Nauk SSSR, 81, 3–184 (1966).

M. Vuorinen, “On the existence of angular limits of n-dimensional quasiconformal mappings,” Ark. Mat., 18, 157–180 (1980).