Constant Scalar Curvature Metrics on Toric Surfaces
Constant Scalar Curvature Metrics on Toric Surfaces
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DOI：
10.1007/s00039-009-0714-y
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发表时间：
2008-05
影响因子：
2.2
通讯作者：
S. Donaldson
中科院分区：
文献类型：
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作者：
S. Donaldson
本文的主要结果是复曲面上常数量曲率Kahler度量的存在性定理，假设流形是K-稳定的。证明建立在作者的早期论文，其中减少了问题的某些先验估计。这些估计是使用黎曼几何和凸分析的参数组合得到的。本文的最后一部分讨论了当K稳定性不成立且解不存在时可能出现的现象。
The main result of the paper is an existence theorem for a constant scalar curvature Kahler metric on a toric surface, assuming the K-stability of the manifold. The proof builds on earlier papers by the author, which reduce the problem to certain a priori estimates. These estimates are obtained using a combination of arguments from Riemannian geometry and convex analysis. The last part of the paper contains a discussion of the phenomena that can be expected when the K-stability does not hold and solutions do not exist.