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Abstract

Let A denote the set of ideal accessible boundary points of a simply connected domain. Recall that these are the finite radial limit points of the Riemann map from the unit disk onto and that each radius along which the limit exists gives a distinct ideal boundary point. In particular, distinct ideal accessible boundary points may have the same complex coordinate. Fix w0 ∈  and for eacha ∈ A andr < |w0 − a| let γ (a, r) ⊂ {z : |z − a| = r} be the circular crosscut of  separatinga fromw0 that can be joined toa by a Jordan arc contained in ∩ {z : |z− a| < r}. Throughout this paper we will refer to γ (a, r) as theprincipal separating arc for a of radiusr. LetL(a, r) denote the Euclidean length of γ (a, r) and let