Smooth and singular Kahler-Einstein metrics
  Smooth Kahler-Einstein metrics have been studied for the past 80 years. More recently, singular Kahler-Einstein metrics have emerged as objects of intrinsic interest, both in differential and algebraic geometry, as well as a powerful tool in better understanding their smooth counterparts. This article is mostly a survey of some of these developments. 
Yanir A. Rubinstein
math.DG math.AG math.AP math.CV