论文标题
横向测量和最佳Lipschitz和最小梯度图
Transverse Measures and Best Lipschitz and Least Gradient Maps
论文作者
论文摘要
在地图从表面到圆圈的地图中，我们表现出最佳Lipschitz（无限谐波）图和最小梯度图之间的双重性。我们表明，鉴于从表面到圆的地图的同质类别类别，无限谐波图定义了表面上的大地层压，而双重最小梯度图定义了层压板上的横向测量。这是迈向瑟斯顿（Thurston）在双曲线表面和瑟斯顿（Teichmueller）空间上瑟斯顿（Thurston）的不对称度量方面的最佳Lipschitz地图上进行分析方法的第一步。
We exhibit the duality between best Lipschitz (infinity harmonic) maps and least gradient maps in the case of maps from surfaces to the circle. We show that given a homotopy class of a map from a surface to the circle the infinity harmonic map defines a geodesic lamination on the surface and the dual least gradient map defines a transverse measure on the lamination. This is the initial step towards an analytic approach to Thurston's work on best Lipschitz maps between hyperbolic surfaces and Thurston's asymmetric metric on Teichmueller space.
