Shadows of Teichmüller Discs in the Curve Graph
Shadows of Teichmüller Discs in the Curve Graph
复制标题
曲线图中 Teichmüller 圆盘的阴影
DOI：
10.1093/imrn/rnw318
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发表时间：
2018
影响因子：
1
通讯作者：
Tang R
中科院分区：
文献类型：
--
作者：
Tang R
我们考虑了与给定的teichm<e:1>椎间盘相关的几种自然曲线集，如收缩集或圆柱集，并研究了它们在曲线图中的粗糙几何形状。我们证明了这些集合是拟凸的，并且在一致有界的Hausdorff距离内一致。我们描述了曲线上的两种操作，并证明了它们近似于各自目标的最近点投影。我们的技术可以用来证明从曲线图到与teichm<s:1> ller圆盘相关的填充多弧图的自然映射的有界测地线像定理。
We consider several natural sets of curves associated to a given Teichmüller disc, such as the systole set or cylinder set, and study their coarse geometry inside the curve graph. We prove that these sets are quasiconvex and agree up to uniformly bounded Hausdorff distance. We describe two operations on curves and show that they approximate nearest point projections to their respective targets. Our techniques can be used to prove a bounded geodesic image theorem for a natural map from the curve graph to the filling multi-arc graph associated to a Teichmüller disc.