Kähler-Einstein Metrics for the Case of Negative and Zero Anticanonical Class
Suppose M is a compact Kähler manifold of complex dimension m. We would like to prove in this chapter the existence of a Kähler-Einstein metric on M when the anticanonical class of M is either negative or zero. A Kähler-Einstein metric means a Kähler metric whose Ricci curvature is a constant multiple of the Kähler metric. First we formulate the problem in the form a Monge-Ampère equation.
KeywordsRicci Curvature Harnack Inequality Zeroth Order Estimate Linear Elliptic Equation Fourth Order Derivative
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