Geodesic
Equilibrium Measures on a Compact Riemann Surface
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics and applications, Tome 306 (2019), pp. 313-351

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Various notions of energy are introduced for charges on a compact Riemann surface that generalize the corresponding notions of logarithmic potential theory in the complex plane. Standard properties of the corresponding equilibrium measures are proved both in the case of measures supported on a given compact set and in the case of measures with arbitrary supports. 
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     author = {E. M. Chirka},
     title = {Equilibrium {Measures} on a {Compact} {Riemann} {Surface}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {313--351},
     publisher = {mathdoc},
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     year = {2019},
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     url = {http://geodesic.mathdoc.fr/item/TM_2019_306_a23/}
}
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E. M. Chirka. Equilibrium Measures on a Compact Riemann Surface. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics and applications, Tome 306 (2019), pp. 313-351. http://geodesic.mathdoc.fr/item/TM_2019_306_a23/