AN ASYMPTOTIC FORMULA FOR THE MINIMAL CAPACITY AMONG SETS OF EQUAL-AREA

We give an asymptotic formula for [GRAPHICS] as epsilon --> 0, involving the geometry of the domain OMEGA. For disks centered at a conformal center the asymptotic behaviour happens to be the same. Thus approximate solutions of the capacity minimization problem for small epsilon are easily computed. This is applicable to various engineering problems. As a byproduct of the above formula we find a branch of hyperbolic solutions of Bernoulli's free-boundary problem concentrating at a conformal center.