| Test Configurations, Stabilities and Canonical Kähler Metrics: Complex Geometry by the Energy Method 2021 Edition Contributor(s): Mabuchi, Toshiki (Author) |
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ISBN: 9811604991 ISBN-13: 9789811604997 Publisher: Springer OUR PRICE: $66.49 Product Type: Paperback Published: March 2021 |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential - Mathematics | Mathematical Analysis - Mathematics | Geometry - Algebraic |
| Physical Information: 0.3" H x 6.14" W x 9.21" (0.45 lbs) 128 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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 K hler 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 K hler metrics. |