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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)

Abstract

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.

Keywords

Ricci Curvature Harnack Inequality Zeroth Order Estimate Linear Elliptic Equation Fourth Order Derivative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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