Szekelyhidi, Gabor 1981
Overview
Works:  2 works in 13 publications in 1 language and 212 library holdings 

Roles:  Author 
Publication Timeline
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Most widely held works by
Gabor Szekelyhidi
An introduction to extremal Kähler metrics by
Gabor Szekelyhidi(
Book
)
10 editions published between 1900 and 2014 in English and held by 209 WorldCat member libraries worldwide
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 higherdimensional generalization of this result in the setting of Kahler geometry. This book gives an introduction to the study of extremal Kahler 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 Kahler 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 KahlerEinstein metrics the Bergman kernel expansion due to Tian Donaldson's lower bound for the Calabi energy and ArezzoPacard's existence theorem for constant scalar curvature Kahler metrics on blowups.  Provided by Publisher
10 editions published between 1900 and 2014 in English and held by 209 WorldCat member libraries worldwide
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 higherdimensional generalization of this result in the setting of Kahler geometry. This book gives an introduction to the study of extremal Kahler 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 Kahler 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 KahlerEinstein metrics the Bergman kernel expansion due to Tian Donaldson's lower bound for the Calabi energy and ArezzoPacard's existence theorem for constant scalar curvature Kahler metrics on blowups.  Provided by Publisher
Extremal metrics and Kstability by
Gabor Szekelyhidi(
Book
)
3 editions published in 2006 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 2006 in English and held by 3 WorldCat member libraries worldwide
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