Kähler-Einstein Metrics for the Case of Negative and Zero Anticanonical Class

  • Yum-Tong Siu
Part of the DMV Seminar book series (OWS, volume 8)


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.


Ricci Curvature Harnack Inequality Zeroth Order Estimate Linear Elliptic Equation Fourth Order Derivative 
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Copyright information

© Birkhäuser Verlag Basel 1987

Authors and Affiliations

  • Yum-Tong Siu
    • 1
  1. 1.Department of Mathematics Science CenterHarvard UniversityCambridgeUSA

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