4 problems

Let $\Omega\subset (\overline{\mathbb{R}}^n,d_s)$ be a domain satisfying the Gehring–Hayman inequality and the ball separation condition. Here, $d_s$ denotes the spherical metric,…

Reflexivity conjecture. The Banach space $X$ is reflexive if and only if each of its open half spaces is geodesic in the quasihyperbolic metric.

Let $G$ be a domain satisfying a $\beta$-quasihyperbolic boundary condition, and let $n$ be the ambient dimension. Set $p=n-n\beta$, where $p\geq 1$. Quasihyperbolic boundary condi…

Väisälä's uniqueness, prolongation and convexity conjectures. There are universal constants $c_u,c_p,c_c>0$ such that: