4 problems

Let a Jordan curve be a simple closed curve $\gamma\subset\mathbb{R}^2$. An isosceles trapezoid is a quadrilateral whose vertices are the intersection set of two parallel lines and…

Let $f\colon S^2\to S^2$ be a Thurston map with a hyperbolic orbifold that is realized by a rational map. Let $P_f$ denote its postcritical set, and let pullbacks be considered up…

Let $(\mathcal X,\mathcal B,\angle)$ be an angle space conformal to a Jordan curve, meaning that it arises from the angle structure induced by a Jordan curve under conformal equiva…

Average-distance conjecture. For any $k$-touching family $\mathcal{F}$ of Jordan curves, the average distance in $\mathcal{F}$ is at most