Abstract
Logarithmic capacity is shown to be minimal for a planar set having N-fold rotational symmetry (\(N \ge 3\)), among all conductors obtained from the set by area-preserving linear transformations. Newtonian and Riesz capacities obey a similar property in all dimensions, when suitably normalized linear transformations are applied to a set having irreducible symmetry group. A corollary is Pólya and Schiffer’s lower bound on capacity in terms of moment of inertia.
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