The Buyarov–Rahmanov formula for external field in the vector extremal logarithmic potential problem

The aim of the paper is to prolong the generalization of the scalar problem Buyarov–Rakhmanov theorem (1999) to vector extremal logarithmic potential problem in the presence of the external field. We consider the generalization in two dimensional extremal problem with Nikishin matrix of interaction. We have got the expressions for dependence of the external field from supports of extremal measures.