The Uniform Version of Yau–Tian–Donaldson Conjecture for Singular Fano Varieties

We prove the following result: if a $$\,\,\,\,\,{\mathbb {Q}}\,\,\,\,\,$$ -Fano variety is uniformly K-stable, then it admits Kähler–Einstein metric. This proves uniform version of Yau–Tian–Donaldson conjecture for all (singular) Fano varieties with discrete automorphism groups. achieve this by modifying Berman–Boucksom–Jonsson’s strategy in smooth case appropriate perturbative arguments. perturbation approach depends on valuative criterion and non-Archimedean estimates, motivated our previous paper.