论文标题
唐纳森（Teichmüller）理论的功能
Donaldson Functional in Teichmüller Theory
论文作者
论文摘要
在本文中，我们定义了唐纳森类型的功能，其欧拉 - 拉格朗格方程是一个微分方程的系统，与希钦的自偶性方程相对应，以适当选择在封闭的riemann表面上选择higgs捆绑包。这种功能的主要挑战是在其定义的自然领域定义时缺乏规律性和缺乏紧凑性。尽管无法直接采用标准的变分方法，但我们提供了适当的分析工具，使唐纳森的功能可以通过变异观点来治疗。我们证明，这种功能性接收到与其全球最小值相对应的独特关键点。这是直接的结果，我们发现这种自以为是的方程式可以接受独特的解决方案。在此事实的几何形状中的应用中，我们获得了封闭的常数平均曲率浸入双曲线歧管（可能不完整）及其模量空间的参数化。
In this paper we define a Donaldson type functional whose Euler-Lagrange equations are a system of differential equations which corresponds to Hitchin's self-duality equations for a suitable choice of Higgs bundle on closed Riemann surfaces. The main challenge of this functional is its lack of regularity and lack of compactness when defined in its natural domain of definition. Though a standard variational approach cannot directly be applied, we provide the appropriate analytical tools that make Donaldson functional treatable by a variational viewpoint. We prove that this functional admits a unique critical point corresponding to its global minimum. As an immediate consequence, we find that this system of self-duality equations admits a unique solution. Among the applications in geometry of this fact, we obtain a parametrization of closed constant mean curvature immersions in hyperbolic manifolds (possibly incomplete), and their moduli spaces.
