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

Abstract

We prove that the partial $C^0$-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.

arXiv commentv3: 24 pages, corrected Proposition 12 in previous version