In this article, we give a new construction of a Kähler-Einstein metric on a smooth projective variety with ample canonical bundle. As a consequence, for a dominant projective morphism with connected fibers such that a general fiber has an ample canonical bundle, and for a positive integer , we construct a canonical singular Hermitian metric on with semipositive curvature in the sense of Nakano.
"Dynamical construction of Kähler-Einstein metrics." Nagoya Math. J. 199 107 - 122, September 2010. https://doi.org/10.1215/00277630-2010-005