The partial $C^0$-estimate along the continuity method

Understand

We prove that the partial $C^0$-estimate holds for metrics along Aubin's continuity method for finding K\"ahler-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 K\"ahler-Einstein metrics.