The first two parts concern distributions of electric charge on conductors in R2 and R3.
For planar continua, upper and lower bounds are given for the growth of the associated Fekete polynomials and potentials. For continua K of capacity 1 whose outer boundary is an analytic Jordan curve, the family of Fekete polynomials is bounded on K.
The difference between the Fekete potential and the equilibrium distribution is estimated with order logN/N.
The work is based on fundamental results of Pommerenke and on potential theory, including the exterior Green function with pole at infinity.
For convex surfaces, and certain smooth surfaces, a similar technique is used and the order 1/x1/2 is obtained.
In the last part, a Nevanlinna-like criterion for positive capacity of Cantor-type sets K is proved. Using this criterion, examples are constructed of such K with capacity zero such that the projections of the square of K in all but two directions have positive capacity.
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