Dimension Drop for Harmonic Measure on Ahlfors Regular Boundaries

Yingying Cai, Xavier Tolsa

We provide quantitative estimates for the dimension drop of harmonic measure. We show that for a domain $\hat{I}\text{c◯}={\mathbb{R}}^{n+1}\setminus E$ where $E$ is an $s$-Ahlfors regular compa…