Local geodesics between toric plurisubharmonic functions with infinite   energy
  Our interest is the behavior of weak geodesics between two plurisubharmonic functions on pseudoconvex domains. We characterize the convergence condition along the geodesic between toric psh functions with a pole at origin on a unit ball in $\mathbb{C}^n$ by means of Lelong numbers. 
Genki Hosono
math.CV