Einstein Manifolds and Extremal Kahler Metrics

Abstract

In joint work with Chen and Weber, the author has elsewhere shown that CP2#2(-CP2) admits an Einstein metric. The present paper gives a new and rather different proof of this fact. Our results include new existence theorems for extremal Kahler metrics, and these allow one to prove the above existence statement by deforming the Kahler-Einstein metric on CP2#3(-CP2) until bubbling-off occurs.