Recording date: 30/08/2011

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### Equilibrium problems for vector potentials with semidefinite interaction matrices and constrained masses

In this talk we prove existence and uniqueness of a solution to the problem of minimizing the logarithmic

energy of vector potentials associated to a d-tuple of positive measures supported on closed subsets of the

complex plane. The assumptions we make on the interaction matrix are weaker than the usual ones and

we also let the masses of the measures vary in a compact subset of Rd

+. We characterize the solution in

terms of variational equations. Finally, we review a few examples taken from the recent literature [1,2,3,4]

that are related to our results.

B. Beckermann

B. Beckermann

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