Families of vector measures which are equilibrium measures in an external field

Abstract

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 and 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 is analysed. Integral formulae recovering the extremal measure with mass from the supports of extremal measures with smaller masses are obtained. Bibliography: 27 titles.