Geodesic
Weighted modules and capacities on a~Riemann surface
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 33, Tome 458 (2017), pp. 164-217

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On a Riemann surface (in the wide sense of the word in the terminology of Hurwitz–Courant) the weighted capacity and module (with a weight of Muokenhoupt) of a condenser with a finite number plates are defined. The equality of the capacity and module of a condenser is proved. This has solved one Dubinin's problem. 
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     author = {P. A. Pugach and V. A. Shlyk},
     title = {Weighted modules and capacities on {a~Riemann} surface},
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P. A. Pugach; V. A. Shlyk. Weighted modules and capacities on a~Riemann surface. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 33, Tome 458 (2017), pp. 164-217. http://geodesic.mathdoc.fr/item/ZNSL_2017_458_a9/