8 problems

Let $G$ be a geometrically finite Bers boundary group, and let $\Lambda(G)$ be its limit set. Form the contact tree whose vertices are the components of the domain of discontinuity…

Let $K_i$, for $i\in\{1,2\}$, be limit sets of hyperbolic conformal dynamical systems, such as limit sets of convex co-compact Kleinian groups or Julia sets of hyperbolic rational…

Let $K_i$, for $i\in\{1,2\}$, be Basilica limit sets of geometrically finite conformal dynamical systems. A map is weakly type-preserving if it sends parabolic points to parabolic…

Let $K_i$, for $i\in\{1,2\}$, be Basilica limit sets of geometrically finite conformal dynamical systems, such as limit sets of geometrically finite Kleinian groups or Julia sets o…

Let $\mathcal{M}$ be the Mandelbrot set, let $\mathcal{H}\subset\mathcal{M}$ be a hyperbolic component, and let $\mathcal{M}_{\mathcal{H}}$ be the associated small copy of…

Let $\mathcal J$ be the Julia set of a rational map and let $\Lambda$ be the limit set of a Kleinian group. Suppose that $\mathcal J$ and $\Lambda$ are connected and neither is hom…

Let $Z$ be a compact metric space that is quasi-Möbius homeomorphic to the boundary of a hyperbolic group, and suppose that $Z$ satisfies the combinatorial Loewner property (CLP).…

Conjecture I. If there exists an automorphism of infinite order $h\in\operatorname{Aut}(\mathbb{C}\setminus A)$ such that the quotient space…