7 problems

Let $(\phi_t)$ be a parabolic semigroup of zero hyperbolic step in the unit disk, with Denjoy–Wolff point $\tau$. The slope is the cluster set of $\arg(1-\overline{\tau}\phi_t(z))$…

Let $\mathbb{D}$ denote the unit disk, and let $G$ be a simply connected subdomain of $\mathbb{D}$. Let $\mathcal{C}$ be the class of domains $\Omega\subset\mathbb{D}$ of the form…

Let $\mathbb{B}^2=\{z\in\mathbb{C}:|z|<1\}$ be the unit disk, and for $a\in\mathbb{B}^2$ define the Möbius transformation … Here $t_{\mathbb{B}^2}$ denotes the $t$-metric on…

Let $\mathbb{B}^2$ be the unit disk, and let $s_{\mathbb{B}^2}$ and $p_{\mathbb{B}^2}$ denote the triangular ratio and point-pair metrics, respectively. For $x,y\in\mathbb{B}^2$, l…

Let $F^N_{n,m}$ be the $L^2$-normalized eigenfunctions of the Neumann Laplace operator on the unit disk, with eigenvalues $\lambda^N_{n,m}$. For a subsequence with…

Dirichlet disk growth conjecture. If $1\leq\gamma<3$, then

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…