Prime ends on the Riemann surfaces

1Ryazanov, VI, 1Volkov, SV
1Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Sloviansk
Dopov. Nac. akad. nauk Ukr. 2017, 9:20-25
https://doi.org/10.15407/dopovidi2017.09.020
Section: Mathematics
Language: English
Abstract: 

We prove criteria for the homeomorphic extension of mappings with finite distortion between the domains on Riemann surfaces to the boundary by prime Carathéodory ends.

Keywords: boundary behavior, homeomorphic extension, mappings of finite distortion, prime Carathéodory ends, Riemann surfaces, Sobolev mappings
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