Shortcuts
Top of page (Alt+0)
Page content (Alt+9)
Page menu (Alt+8)
Your browser does not support javascript, some WebOpac functionallity will not be available.
.
Default
.
PageMenu
-
Main Menu
-
Simple Search
.
Advanced Search
.
Journal Search
.
Refine Search Results
.
Preferences
.
Search Menu
Simple Search
.
Advanced Search
.
New Items Search
.
Journal Search
.
Refine Search Results
.
Bottom Menu
Help
Italian
.
English
.
German
.
New Item Menu
New Items Search
.
New Items List
.
Links
SISSA Library
.
ICTP library
.
Italian National web catalog (SBN)
.
Trieste University web catalog
.
Udine University web catalog
.
© LIBERO v6.4.1sp220816
Page content
You are here
:
>
Search Results
>
System Notification
>
Catalogue Tag Display
Catalogue Card Display
Catalogue Card Display
RAK
Title: Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics ([EBook]) : Delivered at the German Mathematical Society Seminar in Düsseldorf in June, 1986/ by Yum-Tong Siu. Dewey Class: 516 Author: Siu, Yum-Tong., 1943- Publication: Basel : Birkhäuser, 1987. Other name(s): SpringerLink (Online service) Physical Details: 172 pages : online resource. Series: DMV Seminar ;; 8 ISBN: 9783034874861 System details note: Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) Summary Note: 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.: Contents note: 1. The heat equation approach to Hermitian-Einstein metrics on stable bundles -- §1. Definition of Hermitian-Einstein metrics -- §2. Gradient flow and the evolution equation -- §3. Existence of solution of evolution equation for finite time -- §4. Secondary characteristics -- §5. Donaldson’s functional -- §6. The convergence of the solution at infinite time -- Appendix A. Hermitian-Einstein metrics of stable bundles over curves -- Appendix B. Restriction of stable bundles -- 2. Kähler-Einstein metrics for the case of negative and zero anticanonical class -- §1. Monge-Ampère equation and uniqueness -- §2. Zeroth order estimates -- §3. Second order estimates -- §4. Hölder estimates for second derivatives -- §5. Derivation of Harnack inequality by Moser’s iteration technique -- §6. Historical note -- 3. Uniqueness of Kähler-Einstein metrics up to biholomorphisms -- §1. The role of holomorphic vector fields -- §2. Proof of Uniqueness -- §3. Computation of the Differential. -- §4. Computation of the Hessian -- Appendix A. Lower bounds of the Green’s function of Laplacian -- 4. Obstructions to the Existence of Kähler-Einstein Metrics -- §1. Reductivity of automorphism group -- §2. The obstruction of Kazdan-Warner -- §3. The Futaki invariant -- 5. Manifolds with suitable finite symmetry -- §1. Motivation for the use of finite symmetry -- §2. Relation between supM? and infM? -- §3. Estimation of m+?? -- §4. The use of finite group of symmetry -- §5. Applications -- References. ------------------------------ *** There are no holdings for this record *** -----------------------------------------------
Quick Search
Search for