22 mar 2016
Dipartimento di Matematica, Pisa
Abstract.
We survey recent recents concerning Aubin-Yau equations. We introduce the notion of Kähler-Einstein metrics on a compact Kähler manifolds, reduce the existence problem to solving certain complex Monge-Ampère equations. By following a continuity method, the latter will be then reduced to establishing a priori estimates. We will focus on the uniform and C2 estimates which hold in the case of non-positive curvatures.