Skip to main content
SpringerLink
Log in
Birkhäuser
Book cover

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
  • © 1987

Overview

Authors:
  1. Yum-Tong Siu

    1. Department of Mathematics Science Center, Harvard University, Cambridge, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Oberwolfach Seminars (OWS, volume 8)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 79.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (5 chapters)

  1. Front Matter

    Pages 1-10
    Download chapter PDF

  2. The Heat Equation Approach to Hermitian-Einstein Metrics on Stable Bundles

    • Yum-Tong Siu
    Pages 11-84

  3. Kähler-Einstein Metrics for the Case of Negative and Zero Anticanonical Class

    • Yum-Tong Siu
    Pages 85-115

  4. Uniqueness of Kähler-Einstein Metrics up to Biholomorphisms

    • Yum-Tong Siu
    Pages 116-146

  5. Obstuctions to the Existence of Kähler-Einstein Metrics

    • Yum-Tong Siu
    Pages 147-156

  6. Manifolds with Suitable Finite Symmetry

    • Yum-Tong Siu
    Pages 157-167

  7. Back Matter

    Pages 168-172
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics Science Center, Harvard University, Cambridge, USA

    Yum-Tong Siu

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: Yum-Tong Siu

  • Series Title: Oberwolfach Seminars

  • DOI: https://doi.org/10.1007/978-3-0348-7486-1

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1987

  • Softcover ISBN: 978-3-7643-1931-1Published: 01 January 1987

  • eBook ISBN: 978-3-0348-7486-1Published: 06 December 2012

  • Series ISSN: 1661-237X

  • Series E-ISSN: 2296-5041

  • Edition Number: 1

  • Number of Pages: 172

  • Topics: Geometry

Publish with us

Policies and ethics

Back to top

Search

Navigation