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Test Configurations, Stabilities and Canonical Kähler Metrics by Toshiki Mabuchi
Test Configurations, Stabilities and Canonical Kähler Metrics by Toshiki Mabuchi
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Test Configurations, Stabilities and Canonical Kähler Metrics

Complex Geometry by the Energy Method
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Description

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 role in our differential geometric study of stability. By discussing the Chow norm from various points of view, we shall make a systematic study of the existence problem of extremal Kähler metrics.
Release date NZ
March 26th, 2021
Audience
  • Professional & Vocational
Edition
1st ed. 2021
Illustrations
37 Illustrations, black and white; X, 128 p. 37 illus.
Pages
128
ISBN-13
9789811604997
Product ID
34554000

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