Moduli, capacity, BV-functions on the Riemann surfaces
- Authors: Pugach P.1, Shlyk V.1
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Affiliations:
- Department of Computer Science and Customs Information Technologies
- Issue: Vol 38, No 2 (2017)
- Pages: 338-351
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199070
- DOI: https://doi.org/10.1134/S1995080217020172
- ID: 199070
Cite item
Abstract
Let R is a Riemann surface, glued from finitely or countably many domains in the extended complex plane so that the following conditions are satisfied: each point in R projects onto a point w = prW in one on the glued domains, each point in R has a neighbourhood which is a univalent disk, or multivalent disk with the unique ramification point at the centre of disk. We study elementary properties of functions of bounded variation and sets of finite perimeter in an open set Q ⊂ R {W ∈ R: W is a ramification point or prW = ∞}. Further, by using Ziemer’s technique, we obtain the main result
About the authors
P. Pugach
Department of Computer Science and Customs Information Technologies
Author for correspondence.
Email: 679097@mail.ru
Russian Federation, ul. Strelkovaya 16B, Vladivostok, 690034
V. Shlyk
Department of Computer Science and Customs Information Technologies
Email: 679097@mail.ru
Russian Federation, ul. Strelkovaya 16B, Vladivostok, 690034