Infinite geodesic rays in the space of Kahler potentials
  In this paper we explore the connection between special degenerations of algebraic manifolds and geodesics in the space of Kahler metrics. We provide a new and general geometric construction of nontrivial solutions for the geodesic equation. We show how to associate to any special nontrivial degeneration a geodesic of inifite length. 
Claudio Arezzo (1), Gang Tian (2) ((1) Parma - IT, (2) MIT - USA)