Dimension drop for harmonic measure on Ahlfors regular boundaries
classification
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math.APmath.MG
keywords
ahlforsdimensionharmonicmeasureregularboundariesboundarydomain
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We show that given a domain $\Omega\subseteq \mathbb{R}^{d+1}$ with uniformly non-flat Ahlfors $s$-regular boundary and $s\geq d$, the dimension of its harmonic measure is strictly less than $s$.
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