论文标题
测量裤子
Measuring pants
论文作者
论文摘要
我们研究了Lu和Tan证明的双曲线表面身份的术语，即表明它们在长度上单调变化，并且它们验证了某些凸性特性。使用这些属性，我们推断出两个结果。作为第一个应用，我们展示了如何推断出瑟斯顿定理，该定理尤其是针对封闭的双曲线表面，即如果简单的长度频谱“主导”另一个，则实际上两个表面是等距的。作为第二个应用，我们展示了如何在仅取决于边界长度和表面拓扑的边界长度对的上限上找到上限。
We investigate the terms arising in an identity for hyperbolic surfaces proved by Luo and Tan, namely showing that they vary monotonically in terms of lengths and that they verify certain convexity properties. Using these properties, we deduce two results. As a first application, we show how to deduce a theorem of Thurston which states, in particular for closed hyperbolic surfaces, that if a simple length spectrum "dominates" another, then in fact the two surfaces are isometric. As a second application, we show how to find upper bounds on the number of pairs of pants of bounded length that only depend on the boundary length and the topology of the surface.
