There has been fundamental progress in complex differential geometry in the last two decades. For one, The uniformization theory of canonical Kähler metrics has been established in higher dimensions, and many applications have been found, including the use of Calabi-Yau spaces in superstring theory. This monograph gives an introduction to the theory of canonical Kähler metrics on complex manifolds. It also presents some advanced topics not easily found elsewhere.
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"This little monograph offers an essentially self-contained introduction to the theory of canonical Kähler metrics on complex manifolds. ...The author presents some advanced topics which are hard [to] find elsewhere... This graduate course on Kähler-Einstein metrics can be recommended to all those interested in recent developments within complex differential geometry."
--Publicationes Mathematicae
"This monograph includes an essentially self-contained introduction to the theory of canonical Kähler metrics on complex manifolds."
--Zentralblatt Math
The aim of this monograph is to introduce the theory of canonical Kahler metrics on complex manifolds. It also presents the reader with some advanced topics in complex differential geometry which are hard to be found elsewhere. The topics include Calabi-Futaki invariants, extremal Kahler metrics, the Calabi-Yau theorem on existence of Kahler Ricci-flat metrics, and recent progress on Kahler-Einstein metrics with positive scalar curvature.
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