An Introduction to Extremal Kahler Metrics is popular PDF and ePub book, written by Gábor Székelyhidi in 2014-06-19, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, An Introduction to Extremal Kahler Metrics can be Read Online from any device for your convenience.
An Introduction to Extremal Kahler Metrics Book PDF Summary
A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for Riemann surfaces. Extremal metrics were introduced by Calabi as an attempt at finding a higher-dimensional generalization of this result, in the setting of Kähler geometry. This book gives an introduction to the study of extremal Kähler metrics and in particular to the conjectural picture relating the existence of extremal metrics on projective manifolds to the stability of the underlying manifold in the sense of algebraic geometry. The book addresses some of the basic ideas on both the analytic and the algebraic sides of this picture. An overview is given of much of the necessary background material, such as basic Kähler geometry, moment maps, and geometric invariant theory. Beyond the basic definitions and properties of extremal metrics, several highlights of the theory are discussed at a level accessible to graduate students: Yau's theorem on the existence of Kähler-Einstein metrics, the Bergman kernel expansion due to Tian, Donaldson's lower bound for the Calabi energy, and Arezzo-Pacard's existence theorem for constant scalar curvature Kähler metrics on blow-ups.
Detail Book of An Introduction to Extremal Kahler Metrics PDF
- Author : Gábor Székelyhidi
- Release : 19 June 2014
- Publisher : American Mathematical Soc.
- ISBN : 9781470410476
- Genre : Mathematics
- Total Page : 210 pages
- Language : English
- PDF File Size : 18,9 Mb
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