Computation of capacity

Ransford, Thomas; Rostand, Jérémie

doi:10.1090/S0025-5718-07-01941-2

Computation of capacity
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by Thomas Ransford and Jérémie Rostand PDF

Math. Comp. 76 (2007), 1499-1520 Request permission

Abstract:

This article introduces a method for computing upper and lower bounds for the logarithmic capacity of a compact plane set. If the set has the Hölder continuity property, then these bounds converge to the value of the capacity. A number of examples are discussed in detail, including the Cantor middle-third set, for which we estimate $c(E)\approx 0.220949102189507$.

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