10 problems

Let $K\subset\mathbb R^2$ be compact. The logarithmic capacity $\operatorname{Cap}_0(K)$ and Newtonian capacity $\operatorname{Cap}_1(K)$ are the corresponding Riesz capacities. Pó…

Let $\omega$ be a positive superharmonic weight on $\mathbb{D}$, and let $f\in\mathcal{D}_\omega$. Write $[f]_{\mathcal{D}_\omega}$ for the smallest closed shift-invariant subspace…

Let $(\Omega,S,B,\mu)$ be a tree-indexed process. Define … so that $f(n)$ is the probability that a sequence of $n$ IID picks from $\mu$ extends to some sequence in $B$. The conver…

Let $Q_d(p;m)$ and $\widehat Q_d(q;n)$ be the random sets appearing above, and let $A$ be a nonempty target set. In the critical case $2^dpq=1$, the relevant hitting probability is…

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

Let $X$ be a compact subset of $\mathbb{C}$, and let a function space on $X$ admit bounded point derivations, meaning that for some boundary point $x\in X$ and non-negative integer…

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…

Positive-capacity Julia set conjecture. For every such map,

Hutník's conjecture. The class of semicopulas for which, for every $a\in[0,1]$, every measurable space $(X,\mathcal A)\in\mathcal S$, every capacity…

Fleming's conjecture. Fleming conjectured that