Hausdorff Dimension of Harmonic Measure for Self-Conformal Sets

摘要

Under some technical assumptions it is shown that the Hausdorff dimension of theharmonic measure on the limit set of a conformal infinite iterated function system is strictly less than the Hausdorff dimension of the limit set itself if the limit set is contained in a real-analytic curve, if the iterated function system consists of similarities only, or if this system is irregular. As a consequence of this general result the same statement is proven for hyperbolic and parabolic Jul+ia sets, finite parabolic iterated function systems and generalized polynomial-like mappings.