Geodesic
Сondensers and equivalent open sets on a Riemann surface
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 235-260
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Condensers on the compact closure of an open set on a Riemann surface are studied. The equality of the capacity and module of condenser is proved. The definition of NED-sets on the Riemann surface is given and it is proved that NED-sets do not affect the condenser module. Also, a criterion of equivalence of open sets on the Riemann surface is established. 
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P. A. Pugach; V. A. Shlyk. Сondensers and equivalent open sets on a Riemann surface. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 235-260. http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a11/

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