7 problems

Let $\mathbb{B}^n$ be the unit ball, let $\overline{\mathbb{R}}^n$ be the one-point compactification of $\mathbb{R}^n$, and let $q$ denote the chordal metric. For…

Möbius-rigidity conjecture. There is an $a>0$ such that

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…

Möbius covariance conjecture. The entropy transformation

Klén–Vuorinen–Zhang conjecture.

Let $a\in\mathbb{B}^n$ and let $h:\mathbb{B}^n\to\mathbb{B}^n$ be a Möbius transformation of the unit ball onto itself satisfying $h(a)=0$. The distance-ratio metric is denoted by…

Let $A$ be the alphabet, let $A^{\omega}$ denote the set of infinite words over $A$, let $\mathbb{T}$ be the circle, and let $F_{w_{[0,n)}}$ be the Möbius transformation associated…