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On a Fano manifold M we study the supremum of the possible t such that thereis a K\"ahler metric in c_1(M) with Ricci curvature bounded below by t. This isshown to be the same as the maximum existence time of Aubin's continuity pathfor finding K\"ahler-Einstein metrics. We show that on P^2 blown up in onepoint this supremum is 6/7, and we give upper bounds for other manifolds.

Greatest lower bounds on the Ricci curvature of Fano manifolds