Coupled K\"ahler-Einstein metrics
  We propose new types of canonical metrics on K\"ahler manifolds, called coupled K\"ahler-Einstein metrics, generalizing K\"ahler-Einstein metrics. We prove existence and uniqueness results in the cases when the canonical bundle is ample and when the manifold is K\"ahler-Einstein Fano. In the Fano case we also prove that existence of coupled K\"ahler-Einstein metrics imply a certain algebraic stability condition, generalizing $K$-polystability. 
Jakob Hultgren, David Witt Nystr\"om
math.DG math.CV