Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics: Delivered At The German Mathematical Society Seminar In Düsseldorf In June, 1986
Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics: Delivered At The German Mathematical Society Seminar In Düsseldorf In June, 1986
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DOI：
10.1007/978-3-0348-7486-1
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发表时间：
1987
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影响因子：
--
通讯作者：
Y. Siu
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作者：
Y. Siu
这些笔记是根据我在德国数学学会研讨会上发表的演讲在施洛斯米希凯尔恩在杜塞尔多夫6月。1986年关于稳定束的厄米-爱因斯坦度量和卡勒-爱因斯坦度量。这些笔记的目的是用最自然的方法（至少从我自己的主观观点来看）以最简单、最容易理解的形式向读者展示最先进的结果。这些说明中的列报内容相当完备，并将先决条件保持在最低限度。估计中的大多数步骤尽可能地减少到最基本的程序，如分部积分和最大值原理。当使用不太基本的程序，如Sobolev和Calderon-Zygmund不等式和内部Schauder估计。提供参考文献供读者查阅。相当数量的启发式和直观的讨论包括解释为什么某些步骤被使用或某些概念被引入。这种讨论的加入使得演讲的风格在某些地方比通常所期望的严格的演讲更具有对话性。对于稳定丛的Hermitian-Einstein度规问题和Kahler-Einstein度规问题，可以使用连续性方法或热方程方法。这两种方法是如此密切相关，在许多情况下，它们之间的关系几乎是等同的。最重要的是A。先验估计那种脚手架一个挂着一个。
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.