Curvature of the space of stability conditions

Motivated by the study of autoequivalence group triangulated categories via isometric actions on metric spaces, we consider curvature properties (CAT(0), Gromov hyperbolic) space Bridgeland stability conditions with canonical defined Bridgeland. We then prove that is neither CAT(0) nor hyperbolic, and quotient natural $${\mathbb C}$$ -action not in case Kronecker quiver. Moreover, also show hyperbolicity pseudo-Anosov functors Dimitrov–Haiden–Katzarkov–Kontsevich, which yields lower-bound entropy translation length. Finally, curves have been completely classified.