Geodesic
Families of vector measures which are equilibrium measures in an external field
Sbornik. Mathematics, Tome 206 (2015) no. 2, pp. 211-224

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We consider vector extremal problems in the theory of logarithmic potential with external field by looking at an example of two-dimensional problems with Nikishin interaction matrix and variable masses $2x$ and $x$ of the first and second components of the vector measure, respectively. The dependence of the supports of the equilibrium measures, equlibrium constants and energy on the parameter $x$ is analysed. Integral formulae recovering the extremal measure with mass $x$ from the supports of extremal measures with smaller masses are obtained. Bibliography: 27 titles.
Keywords: logarithmic vector potential, extremal vector measure. 
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     title = {Families of vector measures which are equilibrium measures in an external field},
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     url = {http://geodesic.mathdoc.fr/item/SM_2015_206_2_a2/}
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M. A. Lapik. Families of vector measures which are equilibrium measures in an external field. Sbornik. Mathematics, Tome 206 (2015) no. 2, pp. 211-224. http://geodesic.mathdoc.fr/item/SM_2015_206_2_a2/