5 problems

Let $K\subset\mathbb{C}$ be compact and connected with more than one point. Let $M_K$ be the smallest number such that, whenever $p$ has degree $n\geq1$ and $p=p_1\cdots p_m$, … He…

Let $K\subset\mathbb{C}$ be compact and connected, with logarithmic capacity $\operatorname{cap}(K)=1$, $0\in K$, and conformal centroid at the origin. Let $\mu_K$ be the equilibri…

Let $K\subset\mathbb{C}$ be compact and connected, with logarithmic capacity $\operatorname{cap}(K)=1$, $0\in K$, and conformal centroid at the origin. Let $g$ be the Green's funct…

Let $c_1,\ldots,c_{\nu}\in\mathbb C$ be $\nu$ distinct points. For each $\varepsilon>0$, let $\mathbb P_n$ denote the polynomials of degree at most $n$, and let…

Let $K\subset\mathbb{R}^2$ be a compact set of positive capacity, and let a Brownian motion be conditioned on returning to the origin at time $t$. For a disc, let the expected area…