Abstract
We study mappings satisfying some estimate of distortion of modulus of families of paths. Under some conditions on definition and mapped domains, we prove that these mappings are logarithmic Hölder continuous at boundary points.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Cristea, On generalized quasiconformal mappings, Complex Var. Elliptic Equ., 59 (2014), 232–246.
M. Cristea, Boundary behaviour of the mappings satisfying generalized inverse modular inequalities, Complex Var. Elliptic Equ., 60 (2015), 437–469.
M. Cristea, On the lightness of the mappings satisfying generalized inverse modular inequalities, Israel J. Math., 227 (2018), 545–562.
O. Dovhopiatyi, On the possibility of joining two pairs of points in convex domains using paths, Proc. Inst. Appl. Math. Mech., 47 (2023), 3–12.
F. W. Gehring and O. Martio, Quasiextremal distance domains and extension of quasiconformal mappings, J. Anal. Math., 45 (1985), 181–206.
N. S. Ilkevych, E. A. Sevost’yanov and S. A. Skvortsov, On the global behavior of inverse mappings in terms of prime ends, Ann. Fenn. Math., 46 (2021), 371–388.
D. P. Ilyutko and E. A. Sevost’yanov, On prime ends on Riemannian manifolds, J. Math. Sci., 241 (2019), 47–63.
D. A. Kovtonyuk and V. I. Ryazanov, On the theory of prime ends for space mappings, Ukrainian Math. J., 67 (2015), 528–541.
K. Kuratowski, Topology, vol. 2, Academic Press (New York–London, 1968).
O. Martio, S. Rickman and J. Väisälä, Definitions for quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A1, 448 (1969), 1–40.
O. Martio, V. Ryazanov, U. Srebro, and E. Yakubov, Moduli in Modern Mapping Theory, Springer Science + Business Media, LLC (New York, 2009).
O. Martio and J. Sarvas, Injectivity theorems in plane and space, Ann. Acad. Sci. Fenn. Ser. A1 Math., 4 (1978/1979), 384–401.
R. Näkki, Prime ends and quasiconformal mappings, J. Anal. Math., 35, 13–40.
E.A. Poleckii, The modulus method for nonhomeomorphic quasiconformal mappings, Math. USSR-Sb., 12 (1970), 260–270.
S. Rickman, Quasiregular Mappings, Springer-Verlag (Berlin, 1993).
E. A. Sevost’yanov, On logarithmic Hölder continuity of mappings on the boundary, Ann. Fenn. Math., 47 (2022), 251–259.
E. A. Sevost’yanov and S. A. Skvortsov, On the convergence of mappings in metric spaces with direct and inverse modulus conditions, Ukr. Math. J., 70 (2018), 1097–1114.
E. A. Sevost’yanov, S. O. Skvortsov and O. P. Dovhopiatyi, On non-homeomorphic mappings with inverse Poletsky inequality, J. Math. Sci., 252 (2021), 541–557.
J. Väisälä, Lectures on n-dimensional Quasiconformal Mappings, Lecture Notes in Math., vol. 229, Springer-Verlag (Berlin–New York, 1971).
M. Vuorinen, Exceptional sets and boundary behavior of quasiregular mappings in n-space, Ann. Acad. Sci. Fenn. Ser. A1 Math. Dissertationes, (1976), 44 pp.
M. Vuorinen, On the existence of angular limits of n-dimensional quasiconformal mappings, Ark. Math., 18 (1980), 157–180.
M. Vuorinen, Conformal Geometry and Quasiregular Mappings, Lecture Notes in Math., vol. 1319, Springer–Verlag (Berlin, 1988).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Dovhopiatyi, O., Sevost’yanov, E. On boundary Hölder logarithmic continuity of mappings in some domains. Acta Math. Hungar. 172, 499–512 (2024). https://doi.org/10.1007/s10474-024-01419-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-024-01419-w