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Holomorphic Morse Inequalities and Bergman Kernels

2007-12-14 Mathematics
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Release : 2007-12-14
Genre : Mathematics
Kind : eBook
Book Rating : 159/5 ( reviews)

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Book Synopsis Holomorphic Morse Inequalities and Bergman Kernels by : Xiaonan Ma

Download or read book Holomorphic Morse Inequalities and Bergman Kernels written by Xiaonan Ma. This book was released on 2007-12-14. Available in PDF, EPUB and Kindle. Book excerpt: This book examines holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel. It opens perspectives on several active areas of research in complex, Kähler and symplectic geometry. A large number of applications are also included, such as an analytic proof of Kodaira's embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, compactification of complete Kähler manifolds of pinched negative curvature, Berezin-Toeplitz quantization, weak Lefschetz theorems, and asymptotics of the Ray-Singer analytic torsion.

Bergman Kernel Asymptotics and Holomorphic Morse Inequalities

2006
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Release : 2006
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Kind : eBook
Book Rating : 675/5 ( reviews)

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Book Synopsis Bergman Kernel Asymptotics and Holomorphic Morse Inequalities by : Robert Berman

Download or read book Bergman Kernel Asymptotics and Holomorphic Morse Inequalities written by Robert Berman. This book was released on 2006. Available in PDF, EPUB and Kindle. Book excerpt:

Bergman Kernels and Local Holomorphic Morse Inequalities

2002
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Release : 2002
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Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Bergman Kernels and Local Holomorphic Morse Inequalities by : Robert Berman

Download or read book Bergman Kernels and Local Holomorphic Morse Inequalities written by Robert Berman. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt:

Geometric Analysis

2020-04-10 Mathematics
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Release : 2020-04-10
Genre : Mathematics
Kind : eBook
Book Rating : 535/5 ( reviews)

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Book Synopsis Geometric Analysis by : Jingyi Chen

Download or read book Geometric Analysis written by Jingyi Chen. This book was released on 2020-04-10. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are then supplemented by original works that give the more advanced readers a glimpse of the current research in geometric analysis and related PDEs. The book is of significant interest for researchers, including advanced Ph.D. students, working in geometric analysis. Readers who have a secondary interest in geometric analysis will benefit from the survey articles. The results included in this book will stimulate further advances in the subjects: geometric analysis, including complex differential geometry, symplectic geometry, PDEs with a geometric origin, and geometry related to topology. Contributions by Claudio Arezzo, Alberto Della Vedova, Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis, Sun-Yung A. Chang, Zheng-Chao Han, Paul Yang, Tobias Holck Colding, William P. Minicozzi II, Panagiotis Dimakis, Richard Melrose, Akito Futaki, Hajime Ono, Jiyuan Han, Jeff A. Viaclovsky, Bruce Kleiner, John Lott, Sławomir Kołodziej, Ngoc Cuong Nguyen, Chi Li, Yuchen Liu, Chenyang Xu, YanYan Li, Luc Nguyen, Bo Wang, Shiguang Ma, Jie Qing, Xiaonan Ma, Sean Timothy Paul, Kyriakos Sergiou, Tristan Rivière, Yanir A. Rubinstein, Natasa Sesum, Jian Song, Jeffrey Streets, Neil S. Trudinger, Yu Yuan, Weiping Zhang, Xiaohua Zhu and Aleksey Zinger.

An Introduction to Extremal Kahler Metrics

2014-06-19 Mathematics
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Release : 2014-06-19
Genre : Mathematics
Kind : eBook
Book Rating : 478/5 ( reviews)

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Book Synopsis An Introduction to Extremal Kahler Metrics by : Gábor Székelyhidi

Download or read book An Introduction to Extremal Kahler Metrics written by Gábor Székelyhidi. This book was released on 2014-06-19. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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