Lectures on Stability and Constant Scalar Curvature
Lectures on Stability and Constant Scalar Curvature
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DOI：
10.4310/cdm.2007.v2007.n1.a4
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发表时间：
2008-01
期刊：
影响因子：
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通讯作者：
D. Phong;J. Sturm
中科院分区：
文献类型：
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作者：
D. Phong;J. Sturm
介绍了几何不变理论中稳定性的一些最新研究动向和常标量曲率的Kaehler度量问题。除了Chow-Mumford稳定性等经典概念外，重点讨论了几个新的稳定性条件，如K-稳定性、Donaldson无穷维Git以及几乎复结构在微分同胚群下轨道闭合的条件。文中还讨论了相关的分析方法，包括能量泛函估计、Tian-Yau-Zelditch近似、矩映射估计、复Monge-Ampere方程和多势理论以及Kaehler-Ricci流
An introduction is provided to some current research trends in stability in geometric invariant theory and the problem of Kaehler metrics of constant scalar curvature. Besides classical notions such as Chow-Mumford stability, the emphasis is on several new stability conditions, such as K-stability, Donaldson's infinite-dimensional GIT, and conditions on the closure of orbits of almost-complex structures under the diffeomorphism group. Related analytic methods are also discussed, including estimates for energy functionals, Tian-Yau-Zelditch approximations, estimates for moment maps, complex Monge-Ampere equations and pluripotential theory, and the Kaehler-Ricci flow