3 problems

Let $(\phi_t)$ be a non-elliptic semigroup in $\mathbb{D}$ with Koenigs function $h$, and let $\gamma:[0,+\infty)\to\mathbb{D}$ be a regular backward orbit converging to a super-re…

Let $B\subset\mathbb{C}\setminus\{0\}$ be a closed disk and let $D\subset\overline{\mathbb{C}}$ be a domain. Define $k(D,B)$ to be the smallest $k\in[0,1)$ such that every holomorp…

Let $(\phi_t)_{t\geq 0}$ be a one-parameter semigroup of holomorphic self-maps of the unit disk, with boundary Denjoy–Wolff point $\tau$, and let $\Phi=\{\phi_t:t\geq 0\}$. Suppose…