On direct and inverse Poletsky inequalities with a tangential dilatation

References

[1] Ahlfors, L.: Lectures on Quasiconformal Mappings, Van Nostrand, New York, 1966.Search in Google Scholar

[2] Bojarski, B.—Iwaniec, T.: Analytical foundations of the theory of quasiconformal mappings in ℝⁿ, Ann. Acad. Sci. Fenn. Ser. A. I. Math. 8 (1983), 257–324.Search in Google Scholar

[3] Federer, H.: Geometric Measure Theory, Springer, Berlin, 1969.Search in Google Scholar

[4] Gehring, F. W.: Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc. 103 (1962), 353–393.Search in Google Scholar

[5] Golberg, A.—Salimov, R.—Sevost’yanov, E.: Normal families of discrete open mappings with controlled p-module, Contemp. Math. 667 (2016), 83–103.Search in Google Scholar

[6] Hesse, J.: A p-extremal length and p-capacity equality, Ark. Mat. 13 (1975), 131–144.Search in Google Scholar

[7] Ilyutko, D.—Sevost’yanov, E.: Open discrete mappings with unbounded coefficient of quasi-conformality on Riemannian manifolds, Sb. Math. 207 (2016), 65-112.Search in Google Scholar

[8] Ilyutko, D.—Sevost’yanov, E.: Boundary behaviour of open discrete mappings on Riemannian manifolds, Sb. Math. 209 (2018), 605–651.Search in Google Scholar

[9] Kovtonyuk, D.—Ryazanov, V.: New modulus estimates in Orlicz-Sobolev classes, Ann. Univ. Buchar. Math. Ser. 5 (LXIII) (2014), 131–135.Search in Google Scholar

[10] Kovtonyuk, D.—Ryazanov, V.—Salimov, R.—Sevost’yanov, E.: Toward the theory of Orlicz-Sobolev classes, St. Petersburg Math. J. 25 (2014), 929–963.Search in Google Scholar

[11] Kuratowski, K.: Topology, vol. 1, Academic Press, New York, 1968.Search in Google Scholar

[12] Lehto, O.—Virtanen, K.: Quasiconformal Mappings in the Plane, Springer, New York etc., 1973.Search in Google Scholar

[13] Martio, O.—Rickman, S.—Väisälä, J.: Topological and metric properties of quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A. I. 488 (1971), 1–31.Search in Google Scholar

[14] Martio, O.—Ryazanov, V.—Srebro, U.—Yakubov, E.: Moduli in Modern Mapping Theory, Springer Science + Business Media, LLC, New York, 2009.Search in Google Scholar

[15] Martio, O.—Srebro, U.: Periodic quasimeromorphic mappings, J. Anal. Math. 28 (1975), 20–40.Search in Google Scholar

[16] Maz’ja, V.: Sobolev Spaces, Springer-Verlag, Berlin, 1985.Search in Google Scholar

[17] Poleckii, E. A.: The modulus method for nonhomeomorphic quasiconformal mappings, Math. USSR-Sb. 12(2) (1970), 260-270.Search in Google Scholar

[18] Reshetnyak, Yu. G.: Space Mappings with Bounded Distortion . Transl. Math. Monogr., vol. 73, Amer. Math. Soc., Providence, RI 1989.Search in Google Scholar

[19] Rickman, S.: Quasiregular Mappings . Results in Mathematic and Related Areas (3), 26, Springer-Verlag, Berlin, 1993.Search in Google Scholar

[20] Ryazanov, V. I.—Sevost’yanov, E. A.: Equicontinuous classes of ring Q-homeomorphisms, Sib. Math. J. 48 (2007), 1093–1105.Search in Google Scholar

[21] Ryazanov, V.—Srebro, U.—Yakubov, E.: On ring solutions of Beltrami equations, J. Anal. Math. 96 (2005), 117–150.Search in Google Scholar

[22] Ryazanov, V.—Salimov, R.—Yakubov, E.: On Boundary Value Problems for the Beltrami Equations, Contemp. Math. 591 (2013), 211–242.Search in Google Scholar

[23] Saks, S.: Theory of the Integral, Dover Publ. Inc., New York, 1964.Search in Google Scholar

[24] Sevost’yanov, E.—Salimov, R.: On a Väisälä-type inequality for the angular dilatation of mappings and some of its applications, J. Math. Sci. 218 (2016), 69–88.Search in Google Scholar

[25] Salimov, R. R.—Sevost’yanov, E. A.: On equicontinuity of one family of inverse mappings in terms of prime ends, Ukr. Math. J. 70 (2019), 1456–1466.Search in Google Scholar

[26] Sevost’yanov, E: On the local behavior of open discrete mappings from the Orlicz-Sobolev classes, Ukr. Math. J. 68 (2017), 1447–1465.Search in Google Scholar

[27] Sevost’yanov, E. A.: Boundary behavior and equicontinuity for families of mappings in terms of prime ends, St. Petersburg Math. J. 30 (2019), 973–1005.Search in Google Scholar

[28] Sevost’yanov, E.: The inverse Poletsky inequality in one class of mappings, J. Math. Sci. 264 (2022), 455–470.Search in Google Scholar

[29] Sevost’yanov, E.—Salimov, R.—Petrov, E.: On the removable of singularities of the Orlicz-Sobolev classes, J. Math. Sci. 222 (2017), 723–740.Search in Google Scholar

[30] Sevost’yanov, E. A.—Skvortsov, S. A.: On the local behavior of the Orlicz-Sobolev classes, J. Math. Sci. 224 (2017), 563–581.Search in Google Scholar

[31] Stoïlow, S.: Lęcons sur les Principes Topologiques de la Théorie des Fonctions Analytiques, Gauthier-Villars, Paris, 1956.Search in Google Scholar

[32] Shlyk, V. A.: The equality between p-capacity and p-modulus, Sib. Math. J. 34 (1993), 1196-1200.Search in Google Scholar

[33] Väisälä, J.: Lectures on n-Dimensional Quasiconformal Mappings . Lecture Notes in Math. 229, Springer-Verlag, Berlin etc., 1971.Search in Google Scholar

[34] Vuorinen, M.: Exceptional sets and boundary behavior of quasiregular mappings in n-space, Ann. Acad. Sci. Fenn. Ser. A. I. Math. Dissertationes 11 (1976), 1–44.Search in Google Scholar

[35] Ziemer, W. P.: Extremal length and conformal capacity, Trans. Amer. Math. Soc. 126 (1967), 460–473.Search in Google Scholar

[36] Ziemer, W. P.: Extremal length and p-capacity, Michigan Math. J. 16 (1969), 43–51.Search in Google Scholar