Geodesic
Method of interior variations and existence of $S$-compact sets
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 31-58

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The variation of equilibrium energy is analyzed for three different functionals that naturally arise in solving a number of problems in the theory of constructive rational approximation of multivalued analytic functions. The variational approach is based on the relationship between the variation of the equilibrium energy and the equilibrium measure. In all three cases the following result is obtained: for the energy functional and the class of admissible compact sets corresponding to the problem, the arising stationary compact set is fully characterized by a certain symmetry property. 
@article{TM_2012_279_a3,
     author = {V. I. Buslaev and A. Mart{\'\i}nez-Finkelshtein and S. P. Suetin},
     title = {Method of interior variations and existence of $S$-compact sets},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {31--58},
     publisher = {mathdoc},
     volume = {279},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_279_a3/}
}
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V. I. Buslaev; A. Martínez-Finkelshtein; S. P. Suetin. Method of interior variations and existence of $S$-compact sets. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and geometric issues of complex analysis, Tome 279 (2012), pp. 31-58. http://geodesic.mathdoc.fr/item/TM_2012_279_a3/