Test Configurations, Stabilities and Canonical Kähler Metrics
Toshiki Mabuchi
Broschiertes Buch

Test Configurations, Stabilities and Canonical Kähler Metrics

Complex Geometry by the Energy Method

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The Yau-Tian-Donaldson conjecture for anti-canonical polarization was recently solved affirmatively by Chen-Donaldson-Sun and Tian. However, this conjecture is still open for general polarizations or more generally in extremal Kähler cases. In this book, the unsolved cases of the conjecture will be discussed.It will be shown that the problem is closely related to the geometry of moduli spaces of test configurations for polarized algebraic manifolds. Another important tool in our approach is the Chow norm introduced by Zhang. This is closely related to Ding's functional, and plays a crucial ro...