Approximation of weak geodesics and subharmonicity of Mabuchi energy
  We are analysing the convexity and continuity properties of the Mabuchi functional along weak geodesics. The key technical point in our paper is the global approximation of weak geodesics obtained via a well-chosen family of Monge-Amp\`ere equations. 
XiuXiong Chen, Long Li, Mihai Paun
math.DG math.CV