Absolute continuity of harmonic measure for domains with lower regular boundaries

  title={Absolute continuity of harmonic measure for domains with lower regular boundaries},
  author={Murat Akman and Jonas Azzam and Mihalis Mourgoglou},
  journal={Advances in Mathematics},
We study absolute continuity of harmonic measure with respect to surface measure on domains $\Omega$ that have large complements. We show that if $\Gamma\subset \mathbb{R}^{d+1}$ is $d$-Ahlfors regular and splits $ \mathbb{R}^{d+1}$ into two NTA domains then $\omega_{\Omega}\ll \mathscr{H}^{d}$ on $\Gamma\cap \partial\Omega$. This result is a natural generalisation of a result of Wu in [Wu86]. We also prove that almost every point in $\Gamma\cap\partial\Omega$ is a cone point if $\Gamma$ is a… Expand

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