2 problems

Let $G$ be a starlike domain containing the origin, let $d_G(0)$ denote the Euclidean distance from the origin to the boundary of $G$, and let $m$ be a hyperbolic type distance wit…

Let $G\subset\mathbb{R}^n$ be a domain that is starlike with respect to $x\in G$, and let $B_{c_G}(x,r)$ denote the Cassinian ball of radius $r$. Starlikeness conjecture. For every…