A capacity estimate on Carnot groups
The capacity \(\text{cap}_Q(F_1, F_2, N)\) of any condenser \((F_1, F_2, N)\) (where \(N\) is a connected, simply connected compact stratified nilpotent Lie group, \(Q\) is the homogeneous dimension of \(N\), and \(F_1\) and \(F_2\) are closed subsets of \(N\) which satisfy some rather particular conditions) is shown to be bounded from below by a universal positive constant \(\delta\), depending on \(N\) only. Also, some relations between capacities of the form \(\text{cap}_p (\partial U, F, U)\), where \(U\) is an open subset of \(N\), and the Hausdorff dimension of \(F\) are established.
scientific article; zbMATH DE number 833465