Advertisement

© 1987

Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics

Delivered at the German Mathematical Society Seminar in Düsseldorf in June, 1986

Book

Part of the DMV Seminar book series (OWS, volume 8)

Table of contents

About this book

Introduction

These notes are based on the lectures I delivered at the German Mathematical Society Seminar in Schloss Michkeln in DUsseldorf in June. 1986 on Hermitian-Einstein metrics for stable bundles and Kahler-Einstein metrics. The purpose of these notes is to present to the reader the state-of-the-art results in the simplest and the most comprehensible form using (at least from my own subjective viewpoint) the most natural approach. The presentation in these notes is reasonably self-contained and prerequisi tes are kept to a minimum. Most steps in the estimates are reduced as much as possible to the most basic procedures such as integration by parts and the maximum principle. When less basic procedures are used such as the Sobolev and Calderon-Zygmund inequalities and the interior Schauder estimates. references are given for the reader to look them up. A considerable amount of heuristic and intuitive discussions are included to explain why certain steps are used or certain notions introduced. The inclusion of such discussions makes the style of the presentation at some places more conversational than what is usually expected of rigorous mathemtical prese"ntations. For the problems of Hermi tian-Einstein metrics for stable bundles and Kahler-Einstein metrics one can use either the continuity method or the heat equation method. These two methods are so very intimately related that in many cases the relationship betwen them borders on equivalence. What counts most is the a. priori estimates. The kind of scaffolding one hangs the a.

Keywords

Derivation Finite Invariant Manifold Morphism equation function proof

Authors and affiliations

  1. 1.Department of Mathematics Science CenterHarvard UniversityCambridgeUSA

Bibliographic information

  • Book Title Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics
  • Book Subtitle Delivered at the German Mathematical Society Seminar in Düsseldorf in June, 1986
  • Authors Y.-T. Siu
  • Series Title DMV Seminar
  • DOI https://doi.org/10.1007/978-3-0348-7486-1
  • Copyright Information Birkhäuser Basel 1987
  • Publisher Name Birkhäuser Basel
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-7643-1931-1
  • eBook ISBN 978-3-0348-7486-1
  • Edition Number 1
  • Number of Pages , 172
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Geometry
  • Buy this book on publisher's site