Packing Measure Analysis of Harmonic Measure

We show that, for any Jordan domain J in R², harmonic measureis supported by a Borel set of packing dimension 1. We alsoobtain incomplete analogs to the results of Makarov, which connectthe almost everywhere behavior of the derivative near the boundaryfor the conformal mapping function from the unit disk J withthe Hausdorff measure properties of sets supporting the harmonicmeasure.