The CAT(0) geometry of convex domains with the Kobayashi metrics

Jinsong Liu, Hongyu Wang

Let $(\Omega ,K_{\Omega })$ be a convex domain in ${\mathbb{C}}^d$ with the Kobayashi metric $K_{\Omega }$. In this paper we prove that $m$-convexity is a necessary condition for $(\Omega ,K_{\Omega })$ to be CAT(0) if…