Boundary Values in the Geometric Function Theory in Domains with Moving Boundaries

This article addresses the problem of boundary correspondence for a sequence of homeomorphisms that change the capacity of a condenser in a controlled way. To study the overall boundary behavior of these mappings, we introduce some capacity metrics in a sequence of domains with nondegenerate core. Completions with respect to these metrics add to the domains new points called boundary elements. As one of the consequences, we obtain not only sufficient conditions for the global uniform convergence of a sequence of homeomorphisms, but some applications to elasticity theory as well.