3 problems

Let $n\geq 2$. A two-sided NTA domain is a domain in $\mathbb{R}^{n+1}$ whose interior and exterior both satisfy the conditions of a non-tangentially accessible domain, and whose i…

Let $\Omega$ be a one-sided NTA domain, and let $u$ and $v$ be positive harmonic functions as above, vanishing on the relevant portion of the boundary, such that their quotient agr…

The higher-dimensional F. and M. Riesz conjecture. The set $B$ has harmonic measure zero.