Abstract
There exists a Greenian domain $D \subset \mathbb{R}^2$ such that for every set $U$ of attainable minimal Martin boundary points which has null harmonic measure, there exist attainable minimal Martin boundary points $u, \nu \not\in U$ which cannot be connected by an $h$-process in $D$ starting from $u$ and converging to $\nu$.
Citation
Krzysztof Burdzy. "On Brownian Paths Connecting Boundary Points." Ann. Probab. 16 (3) 1034 - 1038, July, 1988. https://doi.org/10.1214/aop/1176991675
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