We partially confirm a conjecture of Donaldson relating the greatest Ricci lower bound to the existence of conical Kähler–Einstein metrics on a Fano manifold . In particular, if is a smooth divisor and the Mabuchi –energy is bounded below, then there exists a unique conical Kähler–Einstein metric satisfying for any . We also construct unique conical toric Kähler–Einstein metrics with and a unique effective –divisor for all toric Fano manifolds. Finally we prove a Miyaoka–Yau-type inequality for Fano manifolds with .
"The greatest Ricci lower bound, conical Einstein metrics and Chern number inequality." Geom. Topol. 20 (1) 49 - 102, 2016. https://doi.org/10.2140/gt.2016.20.49