The partial 𝐶⁰-estimate along the continuity method

We prove that the partial C 0 C^0 -estimate holds for metrics along Aubin’s continuity method for finding Kähler-Einstein metrics, confirming a special case of a conjecture due to Tian. We use the method developed in recent work of Chen-Donaldson-Sun on the analogous problem for conical Kähler-Einstein metrics.