4 problems

Condenser-capacity characterization conjecture. The condition above may give another characterization of those compact sets $K$ that are removable for $W^1_a$.

Let $\Omega$ be a domain in $\mathbb C^n$, let $E\subseteq\Omega$ be a closed subset with locally finite $(2n-1)$-dimensional Hausdorff measure, and let $u$ be a subharmonic functi…

Let $\Omega$ be a smooth bounded domain in $\mathbb R^N$, let $1<p<\infty$, let $p'$ be the conjugate exponent to $p$, and let $K\subset\partial\Omega$ be compact. A compact set…

Jones's conjecture. Every Julia set $\mathcal{J}_c$ of a quadratic polynomial is $CH$-removable.