p Harmonic Measure in Simply Connected Domains

Details p Harmonic Measure in Simply Connected Domains p Harmonic Measure in Simply Connected Domains

2009-01-30

arxiv.org/abs/0902.0013v1

Mathematics

Complex Variables

Scientific paper

We extend to all planar simply connected domains Makarov-type results about the Hausdorff dimension of $p$-harmonic measure pioneered by Lewis and Bennewitz in the context of quasidisks. The key to our analysis is a gradient estimate using the distance to the boundary and constants that only depend on $p$. This is achieved by studying the conformal map from the unit disk to the simply connected domain to construct good quasicurves from a point in the domain to the boundary.

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