Test Configurations, Stabilities and Canonical Kahler Metrics - Complex Geometry by the Energy Method (Paperback, 1st ed. 2021)

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 Kahler 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 Kahler metrics.

General

Imprint:	Springer Verlag, Singapore
Country of origin:	Singapore
Series:	SpringerBriefs in Mathematics
Release date:	March 2021
First published:	2021
Authors:	Toshiki Mabuchi
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	128
Edition:	1st ed. 2021
ISBN-13:	978-981-16-0499-7
Categories:	Books > Science & Mathematics > Mathematics > Numerical analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
LSN:	981-16-0499-1
Barcode:	9789811604997

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