Estimating conformal capacity using asymptotic matching

Conformal capacity is a mathematical quantity relevant to a wide range of physical and mathematical problems and recently there has been a resurgence of interest in devising new methods for its computation. In this paper we show how ideas from matched asymptotics can be used to derive estimates for conformal capacity. The formulas derived here are explicit, and there is evidence that they provide excellent approximations to the exact capacity values even well outside the expected range of validity.