Geodesic
Capacities on a Compact Riemann Surface
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and mathematical physics, Tome 311 (2020), pp. 41-83.

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The properties of the capacity of condensers and capacities of compact sets on a compact Riemann surface are investigated. These properties generalize those of the corresponding objects in the complex plane. Discrete analogs of capacities are defined, and their convergence to the corresponding capacities of compact sets and condensers is proved. 
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E. M. Chirka. Capacities on a Compact Riemann Surface. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and mathematical physics, Tome 311 (2020), pp. 41-83. http://geodesic.mathdoc.fr/item/TM_2020_311_a3/

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