To theory of Q-homeomorphisms in metric spaces

R.R. Salimov (Institute of Applied Mathematics and Mechanics of NAS of Ukraine)

Abstract


We study the problem of continuation on boundary of the so-called Q-homeomorphisms between domains in metric spaces with measures. We obtain conditions for function Q(x) and domain boundary, under which any homeomorphism allows continuous continuation on boundary.

References


Gutlyanskii V., Ryazanov V. "To theory of local behaviour of quasiconformal mappings", Izv. RAN, ser. matem., 1995; 59: pp. 31-58. (in Russian)

Gutlyanskii V., Ryazanov V. "On boundary correspondence under quasiconformal mappings", Ann. Acad. Sci. Fenn. Math., 1996; 21(1): pp. 167-178.

Gutlyanskii V., Martio O., Ryazanov V., Vuorinen M. "Infinitesimal geometry of quasiregular mappings", Ann. Acad. Sci. Fenn. Math., 2000; 25(1): pp. 101-130.

Martio O., Ryazanov V., Srebro U., Yakubov E. "Mappings with finite length distortion", J. d'Anal. Math., 2004; 93: pp. 215-236. doi:10.1007/BF02789308

Martio O., Ryazanov V., Srebro U., Yakubov E. "On Q-homeomorphisms", Ann. Acad. Sci. Fenn., 2005; 30(1): pp. 49-69.

Martio O., Ryazanov V., Srebro U., Yakubov E. "Q-homeomorphisms", Contemp. Math., 2006; 364: pp. 193-203. doi:10.1090/conm/364/06685

Vaisala J. Lectures on n-Dimensional Quasiconformal Mappings, LNM 229, Springer-Verlag, 1971.

Näkki R. "Boundary behavior of quasiconformal mappings in n-space", Ann. Acad. Sci. Fenn. Ser. A1., 1970; 484(1): pp. 1-50.

Heinonen J. Lectures on Analysis on Metric Spaces, Springer-Verlag, New York, 2001. doi:10.1007/978-1-4613-0131-8

Martio O. "Modern tools in the theory of quasiconformal mappings", Texts in Math. Ser. B., Univ. Combra, Dept. Math., Combra, 2000; 27: pp. 1-43.

Kuratowski K. Topology. Vol. 2, 1969. (in Russian)

Federer H. Geometric Measure Theory, Springer, Berlin, 1969.




DOI: https://doi.org/10.15421/240717

  

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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