Conical Metrics on Riemann Surfaces, II: Spherical Metrics
Conical Metrics on Riemann Surfaces, II: Spherical Metrics
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DOI：
10.1093/imrn/rnab011
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发表时间：
2019-06
影响因子：
1
通讯作者：
R. Mazzeo;Xuwen Zhu
中科院分区：
文献类型：
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作者：
R. Mazzeo;Xuwen Zhu
我们继续我们在[34]中开始的关于具有常曲率和孤立圆锥奇点的黎曼曲面的研究。利用推广的单因子配置族理论，我们研究了部分或全部锥角大于$2pi的球锥度量的存在性和形变理论。当数$2$位于拉普拉斯函数的弗里德里希延拓的谱中时，变形被精确地阻挡了。我们的主要结果是，在这种情况下，通过允许锥点分裂来找到解的光滑局部模空间是可能的。这一分析事实反映了[37，38]中的几何结构。
We continue our study, initiated in [34], of Riemann surfaces with constant curvature and isolated conic singularities. Using the machinery developed in that earlier paper of extended configuration families of simple divisors, we study the existence and deformation theory for spherical conic metrics with some or all of the cone angles greater than $2\pi $. Deformations are obstructed precisely when the number $2$ lies in the spectrum of the Friedrichs extension of the Laplacian. Our main result is that, in this case, it is possible to find a smooth local moduli space of solutions by allowing the cone points to split. This analytic fact reflects geometric constructions in [37, 38].