On the theory of the boundary behavior of mappings of the Sovolev class on Riemann surfaces

1Volkov, SV, 1Ryazanov, VY
1Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Sloviansk
Dopov. Nac. akad. nauk Ukr. 2016, 10:5-9
https://doi.org/10.15407/dopovidi2016.10.005
Section: Mathematics
Language: Russian
Abstract: 

In terms of dilatations, a number of criteria for a homeomorphic extension to the boundary of mappings in the Sobolev class between domains on Riemann surfaces are formulated.

Keywords: boundary behavior, homeomorphic extension, Riemann surfaces, Sobolev classes, weakly flat boundaries
References: 
  1. Kovtonyuk D.A., Petkov Y.V., Ryazanov V.Y. Ukr. mat. zhurn., 2011, 63, No 8: 1078-1091 (in Russian).
  2. Kovtonyuk D.A., Petkov Y.V., Ryazanov V.Y. Ukr. mat. zhurn., 2012, 64, No 7: 932-944 (in Russian).
  3. Kovtonyuk D.A., Petkov Y.V., Ryazanov V.Y., Salymov R.R. Alhebra i Analyz, 2013, 25, Iss. 4: 101-124 (in Russian).
  4. Forster O. Rymanovy poverkhnosty, Moscow: Mir, 1980 (in Russian).
  5. Stoylov S. Lektsyy o topolohycheskykh pryntsypakh teoryy analytycheskykh funktsyy, Moscow: Nauka, 1964 (in Russian).
  6. Kovtonyuk D.A., Ryazanov V.Y. Ukr. mat. vestnyk, 2008, 5, No 2: 159-184 (in Russian).
  7. Ryazanov V.Y., Salymov R.R. Ukr. mat. vestnyk, 2007, 4, No 2: 199-234 (in Russian).
  8. Martio O., Ryazanov V., Srebro U., Yakubov E. Moduli in Modern Mapping Theory, New York: Springer, 2009.
  9. Kuratovskyy K. Topolohyya, T. 1, Moscow: Mir, 1966 (in Russian).
  10. Yhnat'ev A. A., Ryazanov V.Y. Ukr. mat. vestnyk, 2005, 2, No 3: 395-417 (in Russian).