Authors:
- The main theme of our book is the very hot issue known as the Yau-Tian-Donaldson conjecture
- As to the Yau-Tian-Donaldson conjecture, we focus on the open case on the existence of extremal Kähler metrics
- In our approach to the existence problem of extremal metrics, we use the Chow norm very effectively
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
About this book
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 Kähler metrics.Reviews
Authors and Affiliations
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Department of Mathematics, Osaka University, Graduate School of Science, Toyonaka, Japan
Toshiki Mabuchi
Bibliographic Information
Book Title: Test Configurations, Stabilities and Canonical Kähler Metrics
Book Subtitle: Complex Geometry by the Energy Method
Authors: Toshiki Mabuchi
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-981-16-0500-0
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2021
Softcover ISBN: 978-981-16-0499-7Published: 26 March 2021
eBook ISBN: 978-981-16-0500-0Published: 25 March 2021
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: X, 128
Number of Illustrations: 37 b/w illustrations
Topics: Differential Geometry, Several Complex Variables and Analytic Spaces, Global Analysis and Analysis on Manifolds, Algebraic Geometry