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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 2, Pages 438–461 (Mi izv1818)  

Potentials and correspondence of boundaries

B. P. Kufarev


Abstract: A theorem on the absolute continuity of $ACL_p$-functions on the level sets of $ACL_q$-functions is proved.
For $ACL_1$-homeomorphisms of plane domains the problem of boundary correspondence along Carathéodory prime ends is studied in connection with the singularities of the potentials of the gradient of these mappings.
Horneomorphisms with a bounded potential of the gradient are introduced – new classes of plane topological mappings for which estimates of the distortion of the relative distance in closed domains are established, and, in particular, the $C$-correspondence of boundaries.
Bibliography: 22 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:2, 417–439

Bibliographic databases:

UDC: 517.51+519.5
MSC: 30A72, 30A90, 31A15
Received: 10.08.1975

Citation: B. P. Kufarev, “Potentials and correspondence of boundaries”, Izv. Akad. Nauk SSSR Ser. Mat., 41:2 (1977), 438–461; Math. USSR-Izv., 11:2 (1977), 417–439

Citation in format AMSBIB
\Bibitem{Kuf77}
\by B.~P.~Kufarev
\paper Potentials and correspondence of boundaries
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 2
\pages 438--461
\mathnet{http://mi.mathnet.ru/izv1818}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=499243}
\zmath{https://zbmath.org/?q=an:0363.31001|0378.31001}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 2
\pages 417--439
\crossref{https://doi.org/10.1070/IM1977v011n02ABEH001729}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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