论文标题
拉伸图和测量层压的分析特性
Analytic properties of Stretch maps and geodesic laminations
论文作者
论文摘要
在1995年的预印本中，威廉·瑟斯顿（William Thurston）概述了基于表面之间地图的Teichmueller理论，该理论可最大程度地减少Lipschitz常数。在本文中，我们继续对最佳Lipschitz地图进行分析研究，这是我们在上一篇论文中开始的。本着无限谐波函数的构建精神，我们获得了最佳的Lipschitz地图U，作为在两个双曲线表面之间的固定同型图中，Schatten-Von Neumann积分的最小化器的极限。我们构造了代数构建的二元函数，该功能最小化了双schatten von-neumann积分，并限制了有梯度属性的有界变异的lie代数值v。本文的主要结果是，该度量的支撑是V的衍生物，位于Thurston构建的规范地球层压板上，并由Gueritaud-Kassel进一步研究。在续集论文中，我们将使用这些结果来研究对双曲线结构的依赖，并构建各种横向测量。这应该提供有关几何形状的信息，并与瑟斯顿学校的结果联系。
In a 1995 preprint, William Thurston outlined a Teichmueller theory for hyperbolic surfaces based on maps between surfaces which minimize the Lipschitz constant. In this paper we continue the analytic investigation into best Lipschitz maps which we began in our previous paper. In the spirit of the construction of infinity harmonic functions, we obtain best Lipschitz maps u as limits of minimizers of Schatten-von Neumann integrals in a fixed homotopy class of maps between two hyperbolic surfaces. We construct Lie algebra valued dual functions which minimize a dual Schatten von-Neumann integral and limit on a Lie algebra valued function v of bounded variation with least gradient properties. The main result of the paper is that the support of the measure which is a derivative of v lies on the canonical geodesic lamination constructed by Thurston and further studied by Gueritaud-Kassel. In the sequel paper we will use these results to investigate the dependence on the hyperbolic structures and construct a variety of transverse measures. This should provide information about the geometry and make contact with results of the Thurston school.
