Kähler-Einstein metrics on singular varieties

Question

Let $X$ be a normal projective variety with klt singularities with numerically trivial canonical divisor $K_X$.

Does there always exist a Kähler-Einstein metric on $X$?

Answer 1

Yes, this is a result of Essydieux-Guedj-Zeriahi: "Singular Kähler-Einstein metrics" J. Amer. Math. Soc. 22 (2009), 607-639.