Partial Differential Equations with Minimal Smoothness and Applications

Volume 42 of the series The IMA Volumes in Mathematics and its Applications pp 89-97

Some Questions Concerning Harmonic Measure

  • Christopher J. BishopAffiliated withDept. of Mathematics, UCLA

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The purpose of this note is to discuss some conjectures concerning harmonic measure. We will start by considering harmonic measure on a simply connected plane domain Ω, but eventually we will also consider some multiply connected and higher dimensional domains. Most of these questions are trivial if ∂Ω has tangents a.e. and many are easy if Ω is only a quasicircle. Thus they are really questions about very non-smooth domains.

Key words

Harmonic measure twist points Hausdorff dimension eigenvalues of Laplacian