3 problems

For a bounded convex set $K\subset\mathbb{C}$, an $epsilon>0$, and a polynomial $p$, let $K_epsilon$ be the $epsilon$-neighborhood of $K$ and let $Z(p,K)$ denote the number of zero…

Let $K\subset\mathbb{C}$ be convex, and let $\epsilon>0$ be given. There exists some constant $C>0$ for which the following holds. Let $g,h\in\mathbb{C}(z)$ be rational functions,…

Let $K\subset\mathbb{C}$ be bounded and convex, and let $\epsilon>0$ be given. There is some constant $C>0$ such that if $k/(n-k)>C$, then $K$ satisfies…