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arXiv · 0902.0013

p Harmonic Measure in Simply Connected Domains

John Lewis·Kaj Nyström·Pietro Poggi-Corradini
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Abstract

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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John Lewis, Kaj Nyström, Pietro Poggi-Corradini. 2009-01-30. p Harmonic Measure in Simply Connected Domains. https://arxiv.org/abs/0902.0013

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