## Variation of the equilibrium measure and the $$S$$-property of a stationary compact set.(English. Russian original)Zbl 1236.31001

Russ. Math. Surv. 66, No. 1, 176-178 (2011); translation from Usp. Mat. Nauk. 66, No. 1, 183-184 (2011).
The main result of this paper states that for energy functional generated by logarithmic and Green kernels (see [N. S. Landkof, Foundations of modern potential theory. Translated from the Russian by A. P. Doohovskoy. Die Grundlehren der mathematischen Wissenschaften. Band 180. Berlin-Heidelberg-New York: Springer-Verlag. X, 424 p. (1972; Zbl 0253.31001)]) and for some special (stationary) class of compact sets the extremal compact set has the $$S$$-property.

### MSC:

 31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions

### Keywords:

equilibrium measure; $$S$$-property of compact set

Zbl 0253.31001
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