论文标题
teichm {ü} ller-randers公制
The Teichm{ü}ller-Randers metric
论文作者
论文摘要
In this paper, we introduce a new asymmetric weak metric on the Teichm{ü}ller space of a closed orientable surface with (possibly empty) punctures.This new metric, which we call the Teichm{ü}ller-Randers metric, is an asymmetric deformation of the Teichm{ü}ller metric, and is obtained by adding to the infinitesimal form of the teichm {ü} ller指标差分1形。 我们研究Teichm {ü} ller-randers度量的基本特性。在确切的1形式的情况下，在两个点之间的任何teichm {ü} ller Geodesic都是独特的Teichm {ü} ller- randers-randers Geodesic。一个特别有趣的案例是，差异1形式（最多是一个因素）与测量叶面相关的极长函数对数的差异。我们表明，在这种情况下，Teichm {ü} ller-randers指标在任何TEICHM {ü} ller Disc中都是不完整的，并且我们在该光盘中以其直接测量的叶子来表征该光盘的地理射线。
In this paper, we introduce a new asymmetric weak metric on the Teichm{ü}ller space of a closed orientable surface with (possibly empty) punctures.This new metric, which we call the Teichm{ü}ller-Randers metric, is an asymmetric deformation of the Teichm{ü}ller metric, and is obtained by adding to the infinitesimal form of the Teichm{ü}ller metric a differential 1-form. We study basic properties of the Teichm{ü}ller-Randers metric. In the case when the 1-form is exact, any Teichm{ü}ller geodesic between two points is a unique Teichm{ü}ller--Randers geodesic between them. A particularly interesting case is when the differential 1-form is (up to a factor) the differential of the logarithm of the extremal length function associated with a measured foliation. We show that in this case the Teichm{ü}ller-Randers metric is incomplete in any Teichm{ü}ller disc, and we give a characterisation of geodesic rays with bounded length in this disc in terms of their directing measured foliations.
