The partial $C^0$-estimate along the continuity method
Abstract: We prove that the partial $C0$-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.
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